# How do you solve using the completing the square method 2x^2 - 4x -1=0?

May 20, 2017

$x = 1 + \sqrt{1.5}$
$x = 1 - \sqrt{1.5}$

#### Explanation:

Given-

$2 {x}^{2} - 4 x - 1 = 0$
$2 {x}^{2} - 4 x = 1$

$\frac{2 {x}^{2}}{2} - \frac{4 x}{2} = \frac{1}{2}$
${x}^{2} - 2 x = 0.5$

${x}^{2} - 2 x + 1 = 0.5 + 1 = 1.5$
${\left(x - 1\right)}^{2} = 1.5$
$x - 1 = \pm \sqrt{1.5}$
$x = 1 \pm \sqrt{1.5}$