Asignatura: Matemáticas
Autor: arletteastorga0129
hace 4 años

formula general por favor
2x² + 6x - 40 = 0

Respuestas

Respuesta dada por: roycroos

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

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

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

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

Entonces en el problema tenemos que: a = 2, b = 6, c = -40

Reemplazamos los coeficientes en la fórmula general:

$\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-(6) \pm \sqrt{(6)^2 - [4(2)(-40)]}}{2(2)}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-6 \pm \sqrt{36 - (-320)}}{4}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-6 \pm \sqrt{356}}{4}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-6 \pm 2\sqrt{89}}{4}}$

$\center \Rightarrow\:\mathrm{x_{1}} \mathrm{= \dfrac{-6 + 2\sqrt{89}}{4}}\\\\\\\center \mathrm{x_{1}} \mathrm{= \dfrac{-6}{4}}+\dfrac{2\sqrt{89}}{4}}\\\\\\\center \boxed{\boxed{\boldsymbol{\mathrm{x_{1}} \mathrm{= \dfrac{-3 + \sqrt{89}}{2}}}}}}$ $\center \Rightarrow\:\mathrm{x_{2}} \mathrm{= \dfrac{-6 - 2\sqrt{89}}{4}}\\\\\\\center \mathrm{x_{2}} \mathrm{= \dfrac{-6}{4}}-\dfrac{2\sqrt{89}}{4}}\\\\\\\center \boxed{\boxed{\boldsymbol{\mathrm{x_{-}} \mathrm{= \dfrac{-3 - \sqrt{89}}{2}}}}}}$