# How do you factor and solve x^2+4x+2=0?

Jul 23, 2016

$x = - 0.586 \text{ or } x = - 3.414$

#### Explanation:

${x}^{2} + 4 x + 2 = 0$ cannot be factored because there are no factors of 2 which add up to 4.

It can be solved by the method of completing the square or the quadratic formula. Completing the square will be easier.

${x}^{2} + 4 x {\textcolor{m a \ge n t a}{+ \left(\frac{4}{2}\right)}}^{2} = - 2 {\textcolor{m a \ge n t a}{+ \left(\frac{4}{2}\right)}}^{2} = - 2 \textcolor{m a \ge n t a}{+ 4} = 2$

${\left(x + 2\right)}^{2} = 2 \text{ square root both sides}$

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

$x = + \sqrt{2} - 2 = \text{ or } x = - \sqrt{2} - 2$

$x = - 0.586 \text{ or } x = - 3.414$