Question

5x²-4x-2=0 Completando el cuadrado​

Answer 1

Respuesta:

Explicación paso a paso:

Solución:

Dada la ecuación 5x²-4x-2=0 se solucionará completando cuadrados:

$5x^2-4x-2=0\\\\x^2-\dfrac{4}{5}x-\dfrac{2}{5}=0\\\\x^2-\dfrac{4}{5}x-\dfrac{2}{5}+\left(\dfrac{2}{5}\right)^2-\left(\dfrac{2}{5}\right)^2=0\\\\\left(x-\dfrac{2}{5}\right)^2-\dfrac{2}{5}-\dfrac{4}{25}=0\\\\\left(x-\dfrac{2}{5}\right)^2=\dfrac{2}{5}+\dfrac{4}{25}\\\\\left(x-\dfrac{2}{5}\right)=\pm\sqrt{\dfrac{14}{25}}\\\\\left(x-\dfrac{2}{5}\right)={\dfrac{\pm\sqrt{14}}{5}}\\\\x_1={\dfrac{\sqrt{14}}{5}}+\dfrac{2}{5}\\\\x_2={\dfrac{-\sqrt{14}}{5}}+\dfrac{2}{5}$