# How do you solve using the completing the square method 5x²+8x-2=0?

Jul 13, 2017

$x = \frac{- 4 + 3 \sqrt{2}}{5}$
$x = \frac{- 4 - 3 \sqrt{2}}{5}$

#### Explanation:

Divide by 5 -->
${x}^{2} + \frac{8 x}{5} = \frac{2}{5}$
${x}^{2} + \frac{8 x}{5} + \frac{16}{25} = \frac{2}{5} + \frac{16}{25}$
${\left(x + \frac{4}{5}\right)}^{2} = \frac{18}{25}$
$x + \frac{4}{5} = \pm \frac{\sqrt{18}}{5} = \pm \frac{3 \sqrt{2}}{5}$
$x = - \frac{4}{5} \pm \frac{3 \sqrt{2}}{5} = \frac{- 4 \pm 3 \sqrt{5}}{5}$
$x 1 = \frac{- 4 + 3 \sqrt{2}}{5}$
$x 2 = \frac{- 4 - 3 \sqrt{2}}{5}$