# How do you solve the equation x^2+4x+2=0 by completing the square?

Jan 11, 2017

$x = - 2 \pm \sqrt{2}$

#### Explanation:

The difference of squares identity can be written:

${a}_{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

Complete the square then use this with $a = \left(x + 2\right)$ and $b = \sqrt{2}$ as follows:

$0 = {x}^{2} + 4 x + 2$

$\textcolor{w h i t e}{0} = {x}^{2} + 4 x + 4 - 2$

$\textcolor{w h i t e}{0} = {\left(x + 2\right)}^{2} - {\left(\sqrt{2}\right)}^{2}$

$\textcolor{w h i t e}{0} = \left(\left(x + 2\right) - \sqrt{2}\right) \left(\left(x + 2\right) + \sqrt{2}\right)$

$\textcolor{w h i t e}{0} = \left(x + 2 - \sqrt{2}\right) \left(x + 2 + \sqrt{2}\right)$

Hence:

$x = - 2 \pm \sqrt{2}$