How do you solve using completing the square method m^2+4m+2=0?

Oct 5, 2016

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

Explanation:

The difference of squares identity can be written:

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

Use this with $a = \left(m + 2\right)$ and $b = \sqrt{2}$ as follows:

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

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

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

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

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

Hence:

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