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

Jun 30, 2015

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

#### Explanation:

For any equation of the form
$\textcolor{w h i t e}{\text{XXXX}}$$a {x}^{2} + b x + c = 0$
the solutions can be obtained using the quadratic formula:
$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
(this formula shows up often enough that it is worth memorizing)

Substituting the values from ${x}^{2} + 4 x + 2 = 0$ for $a , b , \mathmr{and} c$
$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{- 4 \pm \sqrt{{4}^{2} - 4 \left(1\right) \left(2\right)}}{2 \left(1\right)}$

$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{- 4 \pm \sqrt{8}}{2}$

$\textcolor{w h i t e}{\text{XXXX}}$$x = - 2 \pm \sqrt{2}$