Determina USANDO LA FÓRMULA GENERAL la solución de la ecuación
33x - 7 + 10x^2 = 0

Respuestas

Respuesta dada por: roycroos

Recordemos que una ecuación cuadrática tiene la siguiente forma:

$\boxed{\mathrm{\boldsymbol{ax^2+bx+c=0}}}$

Por la fórmula general tenemos que:

$\boldsymbol{\boxed{\mathsf{x_{1,2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}}}$

En el problema tenemos que: a = 33, b = 10, c = -7

Entonces reemplazamos

$\center x_{1,2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\\center x_{1,2}=\dfrac{-(10)\pm \sqrt{(10)^2-[4(33)(-7)]}}{2(33)}\\\\\\\center x_{1,2}=\dfrac{-10\pm \sqrt{100-(-924)}}{66}\\\\\\\center x_{1,2}=\dfrac{-10\pm \sqrt{1024}}{66}\\\\\\\center x_{1,2}=\dfrac{-10\pm32}{66}\\\\\\\\$

$\center \Rightarrow\:x_{1}=\dfrac{-10+32}{66}\\\\\\\center x_{1}=\dfrac{22}{66}\\\\\\ \center x_{1}=\dfrac{{22\!\!\!\!\!\!\!\dfrac{\hspace{0.4cm}}{~}^1}}{66\!\!\!\!\!\!\!\dfrac{\hspace{0.4cm}}{~}_3}\\\\\\\center \boxed{\boxed{\boldsymbol{x_{1}=\dfrac{1}{3}}}}\\\\\\\\$ $\center \Rightarrow\:x_{2}=\dfrac{-10-32}{66}\\\\\\\center x_{2}=\dfrac{-42}{66}\\\\\\\center x_{1}=-\dfrac{{42\!\!\!\!\!\!\!\dfrac{\hspace{0.4cm}}{~}^7}}{66\!\!\!\!\!\!\!\dfrac{\hspace{0.4cm}}{~}_{11}}\\\\\\\center \boxed{\boxed{\boldsymbol{x_{2}=-\dfrac{7}{11}}}}$