{"id":1793,"date":"2021-12-02T16:01:32","date_gmt":"2021-12-02T16:01:32","guid":{"rendered":"https:\/\/blogs.ugto.mx\/rea\/?p=1793"},"modified":"2023-10-03T17:26:18","modified_gmt":"2023-10-03T17:26:18","slug":"clase-digital-5-metodos-de-solucion-de-ecuaciones-de-segundo-grado","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/rea\/clase-digital-5-metodos-de-solucion-de-ecuaciones-de-segundo-grado\/","title":{"rendered":"Clase digital 5: M\u00e9todos de soluci\u00f3n de ecuaciones de segundo grado"},"content":{"rendered":"\n\n\n<div class=\"wp-block-cover\" style=\"min-height:284px;aspect-ratio:unset;\"><span aria-hidden=\"true\" class=\"wp-block-cover__background has-background-dim-40 has-background-dim\"><\/span><img decoding=\"async\" class=\"wp-block-cover__image-background wp-image-1794\" alt=\"\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/azrbfoxp_3i-3.jpg\" style=\"object-position:38% 79%\" data-object-fit=\"cover\" data-object-position=\"38% 79%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"1067\" class=\"wp-block-cover__image-background wp-image-1794\" alt=\"\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/azrbfoxp_3i-3.jpg\" style=\"object-position:38% 79%\" data-object-fit=\"cover\" data-object-position=\"38% 79%\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/azrbfoxp_3i-3.jpg 1600w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/azrbfoxp_3i-3-300x200.jpg 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/azrbfoxp_3i-3-1024x683.jpg 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/azrbfoxp_3i-3-768x512.jpg 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/azrbfoxp_3i-3-1536x1024.jpg 1536w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/azrbfoxp_3i-3-272x182.jpg 272w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><\/noscript><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-text-align-center has-base-3-color has-text-color has-large-font-size wp-block-paragraph\"><br>M\u00e9todos de soluci\u00f3n de ecuaciones de segundo grado<\/p>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"introduccion\">Introducci\u00f3n<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a1Hola! Es un enorme gusto encontrarte nuevamente en este proceso formativo, espero sigas atento a toda la informaci\u00f3n que se muestra en las clases pues son muy importantes para tu educaci\u00f3n, por lo tanto te doy la bienvenida a la quinta clase del curso de \u00c1lgebra II titulada \u201cM\u00e9todos de soluci\u00f3n de ecuaciones de segundo grado\u201d.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Iniciaremos la clase con el concepto de ecuaci\u00f3n y su clasificaci\u00f3n. Teniendo los fundamentos claves, resolveremos ecuaciones de segundo grado seleccionando alguno de los tres m\u00e9todos: f\u00f3rmula general, factorizaci\u00f3n o completando el trinomio cuadrado perfecto.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">De acuerdo a lo anterior, empecemos nuestro trabajo.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"desarrollo-del-tema\">Desarrollo del tema<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Una ecuaci\u00f3n de segundo grado, llamada tambi\u00e9n cuadr\u00e1tica, es toda ecuaci\u00f3n en la cual, una vez simplificada, el mayor exponente de la inc\u00f3gnita es 2. &nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Una ecuaci\u00f3n de la forma&nbsp;<em>ax<sup>2<\/sup>+bx+c=0 <\/em>donde&nbsp;<em>a,b,c \u2208 R y a, \u2260 0<\/em>, es una ecuaci\u00f3n de segundo grado; al t\u00e9rmino ax<sup>2<\/sup>&nbsp;se le llama cuadr\u00e1tico,&nbsp;<em>a bx<\/em>&nbsp;lineal, c el t\u00e9rmino independiente.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Las ecuaciones de segundo grado se clasifican en ecuaciones completas e incompletas.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Completas<\/strong>: Es aquella ecuaci\u00f3n que tiene t\u00e9rmino cuadr\u00e1tico, lineal e independiente.&nbsp;En general toda&nbsp;ecuaci\u00f3n de ese tipo es de la forma:<br><br><em>ax<sup>2<\/sup>+bx+c=0<\/em><br><em>5x<sup>2<\/sup>+4x+1=0<\/em><br><\/li>\n\n\n\n<li><strong>Incompletas<\/strong>: Son ecuaciones que carecen del t\u00e9rmino lineal o del t\u00e9rmino independiente.<br> &#8211; Ecuaci\u00f3n cuadr\u00e1tica pura. Es aquella ecuaci\u00f3n cuadr\u00e1tica que carece del t\u00e9rmino lineal, en&nbsp;general toda ecuaci\u00f3n de ese tipo es de la forma<br><br>    <em>ax<\/em><sup>2<\/sup><em>+c=0<\/em><br>    <em>5x<\/em><sup>2<\/sup><em>-10=0<\/em><br><br>&#8211; <em>Ecuaci\u00f3n cuadr\u00e1tica mixta<\/em>. Es aquella ecuaci\u00f3n cuadr\u00e1tica que carece del t\u00e9rmino independiente, en general toda ecuaci\u00f3n de este tipo tiene la forma:<br><br>   <em>ax<sup>2<\/sup>&nbsp;+bx=0<\/em><br>   <em>4x<sup>2<\/sup>+16x=0<\/em><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Las ecuaciones de segundo grado tienen a lo sumo dos soluciones, tambi\u00e9n se denominan ra\u00edces.&nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"1-1-solucion-de-la-ecuacion-cuadratica-pura-ax2-c-0\">1.1. Soluci\u00f3n de la ecuaci\u00f3n cuadr\u00e1tica pura <em>ax<sup>2<\/sup>+c=0<\/em><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">La soluci\u00f3n de la ecuaci\u00f3n cuadr\u00e1tica pura ax<sup>2<\/sup>+c=0, la puedes obtener si aplicas la propiedad multiplicativa para despejar la variable \u00abx\u00bb ; o tambi\u00e9n si utilizas la factorizaci\u00f3n de diferencia de cuadrados.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Los siguientes ejemplos muestran estos m\u00e9todos de soluci\u00f3n:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Desarrolla la soluci\u00f3n de la ecuaci\u00f3n 5x<sup>2<\/sup>-9=0:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Primero aplica la propiedad aditiva para despejar la constante de la ecuaci\u00f3n<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">5x<sup>2<\/sup>=9<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Luego, aplica la propiedad multiplicativa para despejar la variable:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.02.30.png\" alt=\"\" class=\"wp-image-1795\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"85\" height=\"74\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.02.30.png\" alt=\"\" class=\"wp-image-1795\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Por \u00faltimo, aplica la propiedad de la igualdad (ejecutar una misma operaci\u00f3n en ambos miembros de la ecuaci\u00f3n) para extraer la ra\u00edz cuadrada.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.03.05.png\" alt=\"\" class=\"wp-image-1796\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"228\" height=\"57\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.03.05.png\" alt=\"\" class=\"wp-image-1796\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">De manera an\u00e1loga, desarrolla la soluci\u00f3n de la ecuaci\u00f3n x<sup>2<\/sup>&nbsp;+ 100 = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Primero despeja la constante: x<sup>2&nbsp;<\/sup>-100<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Luego extrae ra\u00edz cuadrada:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.04.31.png\" alt=\"\" class=\"wp-image-1797\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"204\" height=\"62\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.04.31.png\" alt=\"\" class=\"wp-image-1797\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Otro m\u00e9todo de soluci\u00f3n de la ecuaci\u00f3n cuadr\u00e1tica pura ax<sup>2<\/sup>+c=0 es por medio de la factorizaci\u00f3n de diferencia de cuadrados, tal y como se muestra a continuaci\u00f3n:&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Desarrolla la soluci\u00f3n de la ecuaci\u00f3n 9x<sup>2<\/sup>-25 =0 por factorizaci\u00f3n.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Recuerda que una diferencia de cuadrados es el resultado de multiplicar dos binomios conjugados (binomios &nbsp;que son diferentes en un signo).&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">De modo que si aplicas la factorizaci\u00f3n de diferencia de cuadrados a 9x<sup>2<\/sup>-25=0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Obtienes que (3x-5)(3x+5) = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ahora bien, si una multiplicaci\u00f3n es cero, entonces uno o todos los factores son cero. Teniendo como &nbsp;fundamento esta premisa, iguala a cero cada factor<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>3x-5 = 0, 3x+5 = 0<\/em>&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por \u00faltimo, por medio de la propiedad multiplicativa despeja la variable en cada factor:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">De 3x-5 = 0 despeja la variable \u00abx\u00bb<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">por consiguiente x = 5\/3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">De 3x+5 = 0 despeja la variable \u00abx\u00bb<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">por lo tanto x= -5\/3<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"1-2-solucion-de-la-ecuacion-cuadratica-mixta-ax2-bx-0\">1.2. Soluci\u00f3n de la ecuaci\u00f3n cuadr\u00e1tica mixta ax<sup>2<\/sup> + bx = 0<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">La soluci\u00f3n de la ecuaci\u00f3n cuadr\u00e1tica mixta ax<sup>2<\/sup>+bx = 0 a puedes obtener por medio de la factorizaci\u00f3n por factor com\u00fan, recuerda que el factor com\u00fan de un polinomio es el m\u00e1ximo com\u00fan divisor de los t\u00e9rminos del polinomio. A continuaci\u00f3n, se muestra la soluci\u00f3n de este tipo de ecuaci\u00f3n:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Asimila la soluci\u00f3n de la ecuaci\u00f3n cuadr\u00e1tica mixta 3x<sup>2<\/sup>&nbsp;&#8211; 7x = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Primero, identifica que el factor com\u00fan de la ecuaci\u00f3n es \u00abx\u00bb<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por lo que su factorizaci\u00f3n es x(3x &#8211; 7) = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Luego, iguala a cero cada factor: x = 0, 3x-7 = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por \u00faltimo, despeja la variable en cada factor: x = 0, x = 7\/3.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"1-3-solucion-de-la-ecuacion-ax2-bx-c-0-por-factorizacion\">1.3. Soluci\u00f3n de la ecuaci\u00f3n ax<sup>2<\/sup>&nbsp;+bx + c = 0 por factorizaci\u00f3n<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">La soluci\u00f3n de la ecuaci\u00f3n de segundo grado ax<sup>2<\/sup>&nbsp;+bx + c = 0, puede obtenerse por factorizaci\u00f3n del trinomio ax<sup>2<\/sup>&nbsp;+ +bx c &nbsp;tal y como se muestra en los siguientes ejemplos:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Recuerda que el trinomio ax<sup>2<\/sup>&nbsp;+ +bx c puede factorizarse como (mx + p)(nx + q) si:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Factorizas ax<sup>2<\/sup>&nbsp;=(mx)(nx)<br>Factorizas c= (p)(q)<br>Compruebas que (mx)(q)+(nx)(p) =bx<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Los siguientes ejemplos muestran este m\u00e9todo de soluci\u00f3n:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Analiza la soluci\u00f3n de la ecuaci\u00f3n x<sub><sup>2<\/sup><\/sub> \u2212 5x + 6 = 0 por factorizaci\u00f3n:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Factorizaci\u00f3n de x<sup>2<\/sup>&nbsp;= (x)(x)<br>Factorizaci\u00f3n de 6=(-2)(-3)<br>Comprobaci\u00f3n de que (x)(-3)+(x)(-2) = -5x<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por lo tanto, la factorizaci\u00f3n de la ecuaci\u00f3n x<sup>2<\/sup>-5x+6=0 es (x-2)(x-3)=0<br>Luego, iguala a cero cada factor: x \u2212 2 = 0, x \u2212 3 = 0<br>Por \u00faltimo, despeja la variable \u00abx\u00bb en cada factor: x = 2, x=3.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Analiza la soluci\u00f3n de la ecuaci\u00f3n x<sup>2<\/sup>&nbsp;\u2212 3x \u2212 28 = 0 por factorizaci\u00f3n:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Factorizaci\u00f3n de&nbsp;x<sub><sup>2<\/sup><\/sub> = (x)(x)<br>Factorizaci\u00f3n de \u221228 = (-7)(4)&nbsp;&nbsp;<br>Comprobaci\u00f3n de que (x)(4)+(x)(\u22127) = -3x<br><br>La factorizaci\u00f3n de la ecuaci\u00f3n &nbsp;x<sup>2<\/sup>&nbsp;\u22123x-28=0 &nbsp;es &nbsp;(x\u22127)(x+4)&nbsp; = 0&nbsp; &nbsp;&nbsp;<br>Iguala a cero cada uno de los factores: x\u22127 = 0, x+4 = 0<br>Despeja la variable \u00abx\u00bb en cada factor: &nbsp;x = 7, x =\u22124<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Analiza la soluci\u00f3n de la ecuaci\u00f3n 5x<sup>2<\/sup>&nbsp;\u2212 x \u2212 6 = 0 por factorizaci\u00f3n:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Factorizaci\u00f3n de 5x<sup>2<\/sup>&nbsp;= (5x)(x)<br>Factorizaci\u00f3n de &nbsp;\u22126 =(-6)(1)<br>Comprobaci\u00f3n de que (5x)(1)+(x)(\u22126) = -x<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Luego la factorizaci\u00f3n de la ecuaci\u00f3n &nbsp;5x<sup>2<\/sup>&nbsp;\u2212x-6=0 es (5x-6)(x+1)=0&nbsp;<br>Iguala a cero los factores: 5x \u22126 = 0, x + 1= 0<br>Despeja la variable \u00abx\u00bb: x= 6 \/ 5, x=\u22121<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Analiza la soluci\u00f3n de la ecuaci\u00f3n 121x<sup>2<\/sup>&nbsp;\u2212110x + 9 = 0 por factorizaci\u00f3n:<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Factorizaci\u00f3n de 121x<sup>2&nbsp;<\/sup>= (11x)(11x)<br>Factorizaci\u00f3n de 9=(-1)(-9)<br>Comprobaci\u00f3n de que (11x)(\u22129)+(11x)(\u22121) =-110x<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Luego la factorizaci\u00f3n de la ecuaci\u00f3n 121x<sup>2<\/sup>&nbsp;\u2212110x + 9 = 0 es (11x-1)(11x-9) =0<br>Iguala a cero los factores: 11x \u22121=0, 11x \u2212 9= 0<br>Despeja de la variable \u00abx\u00bb: x = 1\/11, x = 9\/11<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Como siguiente actividad, te invito a analizar los siguientes videos en donde se explica las ecuaciones cuadr\u00e1ticas por m\u00e9todo de factorizaci\u00f3n.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/es.khanacademy.org\/math\/algebra\/x2f8bb11595b61c86:quadratic-functions-equations\/x2f8bb11595b61c86:quadratics-solve-factoring\/v\/example-1-solving-a-quadratic-equation-by-factoring\" target=\"_blank\" rel=\"noreferrer noopener\">Resolver cuadr\u00e1ticas por factorizaci\u00f3n.<\/a><\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"\u2705ECUACIONES de SEGUNDO GRADO por FACTORIZACI\u00d3N | ECUACI\u00d3N CUADR\u00c1TICA en 4 MINUTOS| Curso \u00c1LGEBRA\" width=\"1200\" height=\"675\" src=\"https:\/\/www.youtube.com\/embed\/8n3dPktlfaA?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"1-4-solucion-de-la-ecuacion-ax2-bx-c-0-por-el-metodo-de-completar-cuadros\">1.4. Soluci\u00f3n de la ecuaci\u00f3n <strong>ax<sup>2<\/sup>&nbsp;+bx + c = 0<\/strong> por el m\u00e9todo de completar cuadros<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">El m\u00e9todo consiste en transformar la ecuaci\u00f3n ax<sup>2<\/sup>&nbsp;+bx + c = 0 en un trinomio cuadrado perfecto, esto es, un trinomio con dos t\u00e9rminos cuadr\u00e1ticos y un t\u00e9rmino que sean el doble producto de los t\u00e9rminos. Este m\u00e9todo se desarrolla bajo los siguientes pasos:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Como ejemplo, analiza la soluci\u00f3n de la ecuaci\u00f3n 5x<sup>2<\/sup>&nbsp;+ 6x \u22128 = 0 por el m\u00e9todo de completar cuadrados<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Paso 1:&nbsp;<\/strong>Divide los t\u00e9rminos de la ecuaci\u00f3n entre el coeficiente de x<sup>2<\/sup>, en este caso entre 5.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.14.50.png\" alt=\"\" class=\"wp-image-1798\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"719\" height=\"114\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.14.50.png\" alt=\"\" class=\"wp-image-1798\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.14.50.png 719w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.14.50-300x48.png 300w\" sizes=\"auto, (max-width: 719px) 100vw, 719px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><strong>Paso 2:&nbsp;<\/strong>Despeja el t\u00e9rmino constante de la ecuaci\u00f3n, en este caso &#8211; 8\/5.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.15.14.png\" alt=\"\" class=\"wp-image-1799\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"147\" height=\"80\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.15.14.png\" alt=\"\" class=\"wp-image-1799\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><strong>Paso 3:<\/strong>&nbsp;Divide el coeficiente de \u00abx\u00bb entre 2, luego eleva al cuadrado este cociente y lo sumas en ambos miembros de la ecuaci\u00f3n:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.15.43.png\" alt=\"\" class=\"wp-image-1800\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"436\" height=\"173\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.15.43.png\" alt=\"\" class=\"wp-image-1800\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.15.43.png 436w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.15.43-300x119.png 300w\" sizes=\"auto, (max-width: 436px) 100vw, 436px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Suma 9\/25 en ambos miembros de la ecuaci\u00f3n.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.16.07.png\" alt=\"\" class=\"wp-image-1801\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"241\" height=\"75\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.16.07.png\" alt=\"\" class=\"wp-image-1801\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Desarrolla la suma de fracciones que est\u00e1n en el lado derecho de la ecuaci\u00f3n.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.16.31.png\" alt=\"\" class=\"wp-image-1802\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"220\" height=\"161\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.16.31.png\" alt=\"\" class=\"wp-image-1802\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><strong>Paso 4:<\/strong>&nbsp;El trinomio.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.16.53.png\" alt=\"\" class=\"wp-image-1803\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"175\" height=\"76\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.16.53.png\" alt=\"\" class=\"wp-image-1803\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">es cuadrado perfecto y su factorizaci\u00f3n es:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.17.16.png\" alt=\"\" class=\"wp-image-1804\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"152\" height=\"98\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.17.16.png\" alt=\"\" class=\"wp-image-1804\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.17.16.png 152w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.17.16-150x98.png 150w\" sizes=\"auto, (max-width: 152px) 100vw, 152px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><strong>Paso 5:<\/strong>&nbsp;Extrae la ra\u00edz cuadrada en ambos miembros y despeja la variable \u00abx\u00bb:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.17.39.png\" alt=\"\" class=\"wp-image-1805\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"333\" height=\"76\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.17.39.png\" alt=\"\" class=\"wp-image-1805\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.17.39.png 333w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.17.39-300x68.png 300w\" sizes=\"auto, (max-width: 333px) 100vw, 333px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><strong>Paso 6:&nbsp;<\/strong>Llegas a la soluci\u00f3n:&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.18.01.png\" alt=\"\" class=\"wp-image-1806\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"391\" height=\"77\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.18.01.png\" alt=\"\" class=\"wp-image-1806\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.18.01.png 391w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.18.01-300x59.png 300w\" sizes=\"auto, (max-width: 391px) 100vw, 391px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Como segundo ejemplo, analiza la soluci\u00f3n de 9x<sup>2<\/sup>&nbsp;\u2212 2x +1= 0:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Paso 1:&nbsp;<\/strong>Divide los t\u00e9rminos de la ecuaci\u00f3n entre el coeficiente de x<sup>2<\/sup>, en este caso entre 9.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.18.40.png\" alt=\"\" class=\"wp-image-1807\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"166\" height=\"80\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.18.40.png\" alt=\"\" class=\"wp-image-1807\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><strong>Paso 2:&nbsp;<\/strong>Despeja el t\u00e9rmino constante de la ecuaci\u00f3n, en este caso 1\/9.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.19.20.png\" alt=\"\" class=\"wp-image-1808\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"165\" height=\"74\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.19.20.png\" alt=\"\" class=\"wp-image-1808\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><strong>Paso 3:&nbsp;<\/strong>Divide el coeficiente de \u00abx\u00bb entre 2, luego eleva al cuadrado este cociente y lo sumas en ambos miembros de la ecuaci\u00f3n:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.19.46.png\" alt=\"\" class=\"wp-image-1809\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"479\" height=\"76\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.19.46.png\" alt=\"\" class=\"wp-image-1809\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.19.46.png 479w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.19.46-300x48.png 300w\" sizes=\"auto, (max-width: 479px) 100vw, 479px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">El cuadrado de este cociente es:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.21.01.png\" alt=\"\" class=\"wp-image-1810\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"130\" height=\"87\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.21.01.png\" alt=\"\" class=\"wp-image-1810\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Suma 1\/18 en ambos miembros de la ecuaci\u00f3n:&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.21.22.png\" alt=\"\" class=\"wp-image-1811\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"248\" height=\"91\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.21.22.png\" alt=\"\" class=\"wp-image-1811\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Desarrolla la suma de fracciones que est\u00e1n en el lado derecho de la ecuaci\u00f3n:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.21.45.png\" alt=\"\" class=\"wp-image-1812\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"229\" height=\"264\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.21.45.png\" alt=\"\" class=\"wp-image-1812\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><strong>Paso 4:<\/strong>&nbsp;El trinomio.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.22.08.png\" alt=\"\" class=\"wp-image-1813\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"154\" height=\"89\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.22.08.png\" alt=\"\" class=\"wp-image-1813\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Es cuadrado perfecto y su factorizaci\u00f3n es:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.22.30.png\" alt=\"\" class=\"wp-image-1814\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"159\" height=\"85\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.22.30.png\" alt=\"\" class=\"wp-image-1814\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><strong>Paso 5:&nbsp;<\/strong>Extrae la ra\u00edz cuadrada en ambos miembros y despeja la variable \u00abx\u00bb:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.22.53.png\" alt=\"\" class=\"wp-image-1815\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"162\" height=\"89\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.22.53.png\" alt=\"\" class=\"wp-image-1815\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Por lo tanto, la soluci\u00f3n es:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.25.41.png\" alt=\"\" class=\"wp-image-1816\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"126\" height=\"99\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.25.41.png\" alt=\"\" class=\"wp-image-1816\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Como siguiente actividad, te invito a analizar el siguiente video en donde se explica las ecuaciones cuadr\u00e1ticas por el m\u00e9todo de completar el Trinomio Cuadrado Perfecto.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Soluci\u00f3n de una ecuaci\u00f3n de segundo grado completando el trinomio cuadrado perfecto. Ejemplo 1\" width=\"1200\" height=\"675\" src=\"https:\/\/www.youtube.com\/embed\/rULXn3uJDxw?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"1-5-solucion-de-la-ecuacion-ax2-bx-c-0-por-formula-general\">1.5. Soluci\u00f3n de la ecuaci\u00f3n ax<sup>2<\/sup>&nbsp;+bx + c = 0 por f\u00f3rmula general<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Para llegar a la f\u00f3rmula general, aplica el m\u00e9todo de completar cuadrados en la soluci\u00f3n de la ecuaci\u00f3n ax<sup>2<\/sup>&nbsp;+bx + c = 0 &nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Paso 1:&nbsp;<\/strong>Divide los t\u00e9rminos de la ecuaci\u00f3n entre el coeficiente del t\u00e9rmino x<sup>2<\/sup>, en este caso entre&nbsp;<em>a<\/em>.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.27.07.png\" alt=\"\" class=\"wp-image-1817\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"164\" height=\"81\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.27.07.png\" alt=\"\" class=\"wp-image-1817\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><strong>Paso 2:<\/strong>&nbsp;Despeja el t\u00e9rmino constante de la ecuaci\u00f3n, en este:&nbsp;<em>c\/a<\/em>.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.27.34.png\" alt=\"\" class=\"wp-image-1818\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"146\" height=\"86\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.27.34.png\" alt=\"\" class=\"wp-image-1818\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><strong>Paso 3:<\/strong>&nbsp;Divide el coeficiente de \u00abx\u00bb entre 2, luego eleva al cuadrado este cociente y lo sumas en ambos miembros de la ecuaci\u00f3n:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">El coeficiente de \u00abx\u00bb entre 2 es:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.28.01.png\" alt=\"\" class=\"wp-image-1819\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"122\" height=\"81\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.28.01.png\" alt=\"\" class=\"wp-image-1819\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">El cuadrado de este cociente es:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.28.22.png\" alt=\"\" class=\"wp-image-1820\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"133\" height=\"75\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.28.22.png\" alt=\"\" class=\"wp-image-1820\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Suma.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.28.41.png\" alt=\"\" class=\"wp-image-1821\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"61\" height=\"72\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.28.41.png\" alt=\"\" class=\"wp-image-1821\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">en ambos miembros de la ecuaci\u00f3n.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.29.02.png\" alt=\"\" class=\"wp-image-1822\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"267\" height=\"83\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.29.02.png\" alt=\"\" class=\"wp-image-1822\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Desarrolla la suma de fracciones que est\u00e1n en el lado derecho de la ecuaci\u00f3n.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.29.26.png\" alt=\"\" class=\"wp-image-1823\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"282\" height=\"73\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.29.26.png\" alt=\"\" class=\"wp-image-1823\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><strong>Paso 4:<\/strong>&nbsp;El trinomio.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.29.48.png\" alt=\"\" class=\"wp-image-1824\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"158\" height=\"84\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.29.48.png\" alt=\"\" class=\"wp-image-1824\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">es cuadrado perfecto y su factorizaci\u00f3n es:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.30.10.png\" alt=\"\" class=\"wp-image-1825\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"210\" height=\"85\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.30.10.png\" alt=\"\" class=\"wp-image-1825\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><strong>Paso 5:&nbsp;<\/strong>Extrae la ra\u00edz cuadrada en ambos miembros y despeja la variable \u00abx\u00bb:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.30.37.png\" alt=\"\" class=\"wp-image-1826\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"228\" height=\"89\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.30.37.png\" alt=\"\" class=\"wp-image-1826\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Por lo tanto, la soluci\u00f3n es:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.31.53.png\" alt=\"\" class=\"wp-image-1827\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"217\" height=\"82\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.31.53.png\" alt=\"\" class=\"wp-image-1827\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Dando origen a la f\u00f3rmula general:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.32.15.png\" alt=\"\" class=\"wp-image-1828\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"215\" height=\"85\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.32.15.png\" alt=\"\" class=\"wp-image-1828\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<h5 class=\"wp-block-heading\" id=\"1-5-1-discriminante-de-la-ecuacion-de-segundo-grado-ax2-bx-c-0\">1.5.1. Discriminante de la ecuaci\u00f3n de segundo grado ax<sup>2<\/sup>&nbsp;+bx + c = 0<\/h5>\n\n\n\n<p class=\"wp-block-paragraph\">En la f\u00f3rmula general, el radicando b<sup>2<\/sup>&nbsp;\u2212 4.a.c se denomina discriminante de la ecuaci\u00f3n, su valor determina si la ecuaci\u00f3n tiene solo una soluci\u00f3n, y si la soluci\u00f3n es real o compleja.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Si b<sup>2<\/sup>&nbsp;\u2212 4. .ac = 0 &nbsp;la ecuaci\u00f3n tiene una soluci\u00f3n real \u00fanica (la soluci\u00f3n es un n\u00famero real).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Si b<sup>2<\/sup>&nbsp;\u2212 4.a.c &gt; 0 la ecuaci\u00f3n tiene m\u00e1s de una soluci\u00f3n real (la soluci\u00f3n son n\u00fameros reales).<br><br>Si b<sup>2<\/sup>&nbsp;\u2212 4.a.c &lt; 0 la ecuaci\u00f3n tiene soluci\u00f3n compleja (la soluci\u00f3n son n\u00fameros complejos).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A continuaci\u00f3n, se presentan varios ejemplos del uso del discriminante b<sup>2<\/sup>&nbsp;\u2212 4.a.c .<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Como primer ejemplo, verifica si la ecuaci\u00f3n tiene soluci\u00f3n real 5x<sup>2<\/sup>&nbsp;\u2212 2x \u22121= 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Primero identifica los coeficientes de los t\u00e9rminos de la ecuaci\u00f3n: a = 5, b =\u22122, c =\u22121<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Luego aplica la propiedad de sustituci\u00f3n en el discriminante b<sup>2<\/sup>&nbsp;\u2212 4.a.c:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.33.18.png\" alt=\"\" class=\"wp-image-1829\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"421\" height=\"63\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.33.18.png\" alt=\"\" class=\"wp-image-1829\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.33.18.png 421w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.33.18-300x45.png 300w\" sizes=\"auto, (max-width: 421px) 100vw, 421px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Concluye que como 24 &gt; 0, la ecuaci\u00f3n tiene soluci\u00f3n real.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Como segundo ejemplo, verifica si la ecuaci\u00f3n.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.33.45.png\" alt=\"\" class=\"wp-image-1830\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"542\" height=\"92\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.33.45.png\" alt=\"\" class=\"wp-image-1830\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.33.45.png 542w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.33.45-300x51.png 300w\" sizes=\"auto, (max-width: 542px) 100vw, 542px\" \/><\/noscript><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.34.05.png\" alt=\"\" class=\"wp-image-1831\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"803\" height=\"89\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.34.05.png\" alt=\"\" class=\"wp-image-1831\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.34.05.png 803w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.34.05-300x33.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.34.05-768x85.png 768w\" sizes=\"auto, (max-width: 803px) 100vw, 803px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Luego aplica la propiedad de sustituci\u00f3n en el discriminante b<sup>2<\/sup>&nbsp;\u2212 4.a.c:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.34.29.png\" alt=\"\" class=\"wp-image-1832\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"514\" height=\"90\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.34.29.png\" alt=\"\" class=\"wp-image-1832\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.34.29.png 514w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.34.29-300x53.png 300w\" sizes=\"auto, (max-width: 514px) 100vw, 514px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Concluye que como:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.34.55.png\" alt=\"\" class=\"wp-image-1833\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"74\" height=\"70\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.34.55.png\" alt=\"\" class=\"wp-image-1833\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">la ecuaci\u00f3n tiene soluci\u00f3n real.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\" id=\"1-5-2-formula-general\">1.5.2. F\u00f3rmula general<\/h5>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.35.39.png\" alt=\"\" class=\"wp-image-1834\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"218\" height=\"93\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.35.39.png\" alt=\"\" class=\"wp-image-1834\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Cuando apliques la f\u00f3rmula general:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.36.21.png\" alt=\"\" class=\"wp-image-1835\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"247\" height=\"96\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.36.21.png\" alt=\"\" class=\"wp-image-1835\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">es necesario que ordenes con respecto a \u00abx\u00bb la ecuaci\u00f3n, esto es, que tenga la presentaci\u00f3n ax<sup>2<\/sup>&nbsp;+bx + c = 0. A continuaci\u00f3n, se muestra la aplicaci\u00f3n de la f\u00f3rmula general:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Como primer ejemplo, analiza la soluci\u00f3n de la ecuaci\u00f3n 2x<sup>2<\/sup>&nbsp;+ 2x + 5 = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Primero identifica que en la ecuaci\u00f3n: a = 2, b = 2, c = 5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Luego aplica la propiedad de sustituci\u00f3n en la f\u00f3rmula general:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.37.02.png\" alt=\"\" class=\"wp-image-1836\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"662\" height=\"259\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.37.02.png\" alt=\"\" class=\"wp-image-1836\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.37.02.png 662w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.37.02-300x117.png 300w\" sizes=\"auto, (max-width: 662px) 100vw, 662px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Y llega a la soluci\u00f3n:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.37.28.png\" alt=\"\" class=\"wp-image-1837\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"290\" height=\"367\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.37.28.png\" alt=\"\" class=\"wp-image-1837\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.37.28.png 290w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.37.28-237x300.png 237w\" sizes=\"auto, (max-width: 290px) 100vw, 290px\" \/><\/noscript><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.37.52.png\" alt=\"\" class=\"wp-image-1838\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"813\" height=\"398\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.37.52.png\" alt=\"\" class=\"wp-image-1838\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.37.52.png 813w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.37.52-300x147.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.37.52-768x376.png 768w\" sizes=\"auto, (max-width: 813px) 100vw, 813px\" \/><\/noscript><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.38.15.png\" alt=\"\" class=\"wp-image-1839\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"556\" height=\"408\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.38.15.png\" alt=\"\" class=\"wp-image-1839\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.38.15.png 556w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.38.15-300x220.png 300w\" sizes=\"auto, (max-width: 556px) 100vw, 556px\" \/><\/noscript><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.38.36.png\" alt=\"\" class=\"wp-image-1840\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"853\" height=\"161\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.38.36.png\" alt=\"\" class=\"wp-image-1840\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.38.36.png 853w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.38.36-300x57.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.38.36-768x145.png 768w\" sizes=\"auto, (max-width: 853px) 100vw, 853px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Como tercer ejemplo, resuelve por f\u00f3rmula general la ecuaci\u00f3n&nbsp;<em>2.i.x<sup>2<\/sup>&nbsp;+ 3x + 5.i = 0<\/em>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;Primero identifica que en la ecuaci\u00f3n: a = 2.i, b = 3, c = 5.i<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.39.10.png\" alt=\"\" class=\"wp-image-1841\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"806\" height=\"485\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.39.10.png\" alt=\"\" class=\"wp-image-1841\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.39.10.png 806w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.39.10-300x181.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.39.10-768x462.png 768w\" sizes=\"auto, (max-width: 806px) 100vw, 806px\" \/><\/noscript><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.39.35.png\" alt=\"\" class=\"wp-image-1842\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"367\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.39.35.png\" alt=\"\" class=\"wp-image-1842\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.39.35.png 800w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.39.35-300x138.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-23-a-las-13.39.35-768x352.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Como siguiente actividad, te invito a analizar los siguientes videos en donde se explica las ecuaciones cuadr\u00e1ticas por el m\u00e9todo de f\u00f3rmula general.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"ECUACIONES CUADR\u00c1TICAS POR F\u00d3RMULA GENERAL - Ejercicio 1\" width=\"1200\" height=\"900\" src=\"https:\/\/www.youtube.com\/embed\/xmzG2xR-oBI?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"conclusion\">Conclusi\u00f3n<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">En conclusi\u00f3n, las funciones cuadr\u00e1ticas son ampliamente usadas en la ciencia, los negocios y la ingenier\u00eda. La gr\u00e1fica de una ecuaci\u00f3n cuadr\u00e1tica en un plano cartesiano nos da como resultado la par\u00e1bola, donde la intersecci\u00f3n con el eje \u201cx\u201d representa la soluci\u00f3n. Esta secci\u00f3n c\u00f3nica con forma de U puede describir trayectorias de chorros de agua en una fuente y el botar de una pelota; graficar el curso de objetos en movimiento, o pueden ser incorporadas en estructuras como reflectores parab\u00f3licos que forman la base de los platos satelitales o faros de los carros.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Las funciones cuadr\u00e1ticas ayudan a predecir ganancias y p\u00e9rdidas en los negocios, y asistir en la determinaci\u00f3n de valores m\u00ednimos y m\u00e1ximos (maximizar ganancias y minimizar costos en un proyecto).&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Muchos de los objetos que usamos hoy en d\u00eda, desde los autom\u00f3viles hasta los relojes, no existir\u00edan si alguien, en alguna parte, no hubiera aplicado una ecuaci\u00f3n cuadr\u00e1tica para su dise\u00f1o.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Llegamos al final de la clase, \u00a1Te felicito por tu buen desempe\u00f1o! Te recuerdo que para dar pleno cierre a esta clase, realices y mandes la tarea asignada. Te encuentro en la sexta sesi\u00f3n, hasta pronto.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"fuentes-de-informacion\">Fuentes de informaci\u00f3n<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Aguilar, A. (2009). Matem\u00e1ticas Simplificadas. (2a ed.). M\u00e9xico: Pearson. Cap. 10, pp. 454-474, 497-511<\/li>\n\n\n\n<li>Baldor, A. (2017). \u00c1lgebra. (3a ed.). M\u00e9xico: Grupo Editorial Patria. Cap. XXXIII, pp. 446-459<\/li>\n\n\n\n<li>Alberro, A., Benjumeda, F., &amp; Garc\u00eda, R. (2013). Matem\u00e1ticas 1. M\u00e9xico: SM. Pp. 207-230<\/li>\n\n\n\n<li>Araya, J. A., Murillo, M., &amp; Soto, A. (2000). Matem\u00e1tica b\u00e1sica con aplicaciones. Costa Rica: EUNED. Cap. 2, pp. 62-65<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Introducci\u00f3n \u00a1Hola! Es un enorme gusto encontrarte nuevamente en este proceso formativo, espero sigas atento a toda la informaci\u00f3n que se muestra en las clases pues son muy importantes para tu educaci\u00f3n, por lo tanto te doy la bienvenida a la quinta clase del curso de \u00c1lgebra II titulada \u201cM\u00e9todos de soluci\u00f3n de ecuaciones de &#8230; <a title=\"Clase digital 5: M\u00e9todos de soluci\u00f3n de ecuaciones de segundo grado\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/rea\/clase-digital-5-metodos-de-solucion-de-ecuaciones-de-segundo-grado\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 5: M\u00e9todos de soluci\u00f3n de ecuaciones de segundo grado\">Leer m\u00e1s<\/a><\/p>\n","protected":false},"author":142,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","episode_type":"","audio_file":"","podmotor_file_id":"","podmotor_episode_id":"","cover_image":"","cover_image_id":"","duration":"","filesize":"","filesize_raw":"","date_recorded":"","explicit":"","block":"","itunes_episode_number":"","itunes_title":"","itunes_season_number":"","itunes_episode_type":"","footnotes":""},"categories":[83,84],"tags":[41,85,86],"class_list":["post-1793","post","type-post","status-publish","format-standard","hentry","category-bachillerato-general","category-algebra-ii","tag-clase-digital","tag-neba04002","tag-sandra-patricia-arriaga-martinez"],"acf":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/1793","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/users\/142"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/comments?post=1793"}],"version-history":[{"count":4,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/1793\/revisions"}],"predecessor-version":[{"id":29837,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/1793\/revisions\/29837"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/media?parent=1793"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/categories?post=1793"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/tags?post=1793"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}