Question

Cual es el resultado de
x²+4x–2=0

Answer 1

SOLUCIÓN

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                                  $Sea\:la\:ecuaci\'on\:cuadr\'atica:\\\\\\ax^2+bx+c=0\\\\\\Por\:f\'ormula\:general\:tenemos\:que:\\\\\\\mathrm{\boxed{x_{1,2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}}\\\\\\Del\:problema:\\\\\\a=1,b=4,c=-2\\\\\\ Entonces\:reemplazamos\\\\\\x_{1,2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x_{1,2}=\dfrac{-(4)\pm \sqrt{(4)^2-[4(1)(-2)]}}{2(1)}\\\\\\x_{1,2}=\dfrac{-4\pm \sqrt{16-(-8)}}{2}\\\\\\x_{1,2}=\dfrac{-4\pm \sqrt{24}}{2}\\\\\\x_{1,2}=\dfrac{-4\pm4.89898}{2}$

                                $\Rightarrow\:x_{1}=\dfrac{-4+4.89898}{2}\\\\\\x_{1}=\dfrac{0.898979}{2}\\\\\\\boxed{\boldsymbol{x_{1}=0.44949}}\\\\\\\Rightarrow\:x_{2}=\dfrac{-4-4.89898}{2}\\\\\\x_{2}=\dfrac{-8.89898}{2}\\\\\\\boxed{\boldsymbol{x_{2}=-4.44949}}$