# How do you solve x^2+8x+7=0 by factoring?

Oct 29, 2017

$x \in \left\{- 7 , - 1\right\}$

#### Explanation:

Separate the middle term into two terms which will match the first and third terms:

${x}^{2} + 8 x + 7 = 0$

${x}^{2} + x + 7 x + 7 = 0$

$\left({x}^{2} + x\right) + \left(7 x + 7\right) = 0$

$x \left(x + 1\right) + 7 \left(x + 1\right) = 0$

$\left(x + 7\right) \left(x + 1\right) = 0$

Therefore:

$x + 7 = 0 \text{ " or " } x + 1 = 0$

$x = - 7 \text{ " or " } x = - 1$