# How do you solve x² - 8 = -7x?

Jul 18, 2016

$x = 1$ or $x = - 8$

#### Explanation:

${x}^{2} - 8 = - 7 x$

$\Leftrightarrow {x}^{2} + 7 x - 8 = 0$

$\Leftrightarrow {x}^{2} + 8 x - x - 8 = 0$

$\Leftrightarrow x \left(x + 8\right) - 1 \left(x + 8\right) = 0$

$\Leftrightarrow \left(x - 1\right) \left(x + 8\right) = 0$

And hence either $x - 1 = 0$ i.e. $x = 1$ or

$x + 8 = 0$ i.e. $x = - 8$.