Question

Resuelve las siguientes ecuaciones cuadraticas por el metodo que prefieras X a la segunda potencia +2x-8=0

Answer 1

SOLUCIÓN

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                     $Sea\:la\:ecuaci\'on\:cuadr\'atica:\\\\ax^2+bx+c=0\\\\Por\:f\'ormula\:general\:tenemos\:que:\\\\\mathrm{\boxed{x_{1,2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}}\\\\\\Del\:problema:\\\\a=1,b=2,c=-8\\\\ Entonces\:reemplazamos\\\\\\x_{1,2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x_{1,2}=\dfrac{-(2)\pm \sqrt{(2)^2-[4(1)(-8)]}}{2(1)}\\\\\\x_{1,2}=\dfrac{-2\pm \sqrt{4-(-32)}}{2}\\\\\\x_{1,2}=\dfrac{-2\pm \sqrt{36}}{2}\\\\\\x_{1,2}=\dfrac{-2\pm6}{2}$

                  $\Rightarrow\:x_{1}=\dfrac{-2+6}{2}\\\\\\x_{1}=\dfrac{4}{2}\\\\\\\boxed{\boldsymbol{x_{1}=2}}\\\\\\\Rightarrow\:x_{2}=\dfrac{-2-6}{2}\\\\\\x_{2}=\dfrac{-8}{2}\\\\\\\boxed{\boldsymbol{x_{2}=-4}}$

Answer 2

x^2 + bx + c

X^2 + 2x - 8 = 0

(x + 4 ) ( x - 2 ) = 0

1) x + 4 = 0

x = -4

2) x - 2 = 0

x = 2