Asignatura: Matemáticas
Autor: albap5270
hace 4 años

2x²+2x+3=0
Resolver con fórmula general

Respuestas

Respuesta dada por: roycroos

╔═════════════════════════════════════════════╗ $\center \mathrm{Una ecuaci\'on cuadr\'atica de la forma:}$

$\mathrm{ax^2 + bx + c=0\:\:donde\:\: a \neq 0}$

$\center \mathrm{Poseer\'a 2 soluciones x_1} \:\mathrm{y\:x_2,\:las\:cuales\:determinaremos\:por:}$

$\boldsymbol{{\mathrm{x_{1,2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}}} \Rightarrow \boxed{\mathrm{F\'ormula\:general}}$ ╚═════════════════════════════════════════════╝

En el problema

$\mathsf{\underbrace{\boldsymbol{2}}_{a}x^2\:+\:\underbrace{\boldsymbol{2}}_{b}x\:+\:\underbrace{\boldsymbol{3}}_{c}=0}$

Entonces a = 2, b = 2, c = 3

Reemplazamos los coeficientes en la fórmula general:

$\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-(2) \pm \sqrt{(2)^2 - [4(2)(3)]}}{2(2)}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-2 \pm \sqrt{4 - (24)}}{4}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-2 \pm \sqrt{-20}}{4}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-2 \pm 4.47214i}{4}}\\\\\\\\$

$\center \Rightarrow\:\mathrm{x_{1}} \mathrm{= \dfrac{-2 + 4.47214i}{4}}\\\\\\\center \mathrm{x_{1}} \mathrm{= \dfrac{-2}{4} + \dfrac{4.47214i}{4}}\\\\\\\center \boxed{\boxed{\boldsymbol{\mathrm{x_{1}} \mathrm{= -0.5 + 1.11803i}}}}\\\\\\\\$ $\center \Rightarrow\:\mathrm{x_{2}} \mathrm{= \dfrac{-2 - 4.47214i}{4}}\\\\\\\center \mathrm{x_{2}} \mathrm{= \dfrac{-2}{4} - \dfrac{4.47214i}{4}}\\\\\\\center \boxed{\boxed{\boldsymbol{\mathrm{x_{2}} \mathrm{= -0.5 - 1.11803i}}}}$