# How do you solve  x^2 – 8x = –16 by completing the square?

Aug 1, 2017

$x = 4 \text{ multiplicity 2}$

#### Explanation:

$\text{rearrange and equate to zero}$

$\Rightarrow {x}^{2} - 8 x + 16 = 0$

$\text{completing the square involves adding half the coefficient}$
$\text{of the x-term squared to } {x}^{2} - 8 x$

$\text{that is } {\left(- 4\right)}^{2} = 16$

${x}^{2} - 8 x + 16 \text{ is already in that form}$

$\Rightarrow {\left(x - 4\right)}^{2} = 0$

$\Rightarrow x = 4 \text{ of multiplicity 2}$