# How do you factor and solve r^2+8r+14=0?

Jul 12, 2016

$x = - 4 \pm \sqrt{2}$

#### Explanation:

$y = {r}^{2} + 8 r + 14 = 0$
$D = {d}^{2} = {b}^{2} - 4 a c = 64 - 56 = 8$ --> $d = \pm 2 \sqrt{2}$
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = - \frac{8}{2} \pm \frac{2 \sqrt{2}}{2} = - 4 \pm \sqrt{2}$
$y = \left(x - x 1\right) \left(x - x 2\right) = \left(x + 4 - \sqrt{2}\right) \left(x + 4 + \sqrt{2}\right)$