# How do you solve x^2 - 6x = 16 by completing the square?

Sep 3, 2017

$x = - 2 \text{ or } x = 8$

#### Explanation:

$\text{to complete the square}$

add (1/2" coefficient of x-term")^2" to both sides"

$\text{that is add "(-6/2)^2=9" to both sides}$

$\Rightarrow {x}^{2} + 2 \left(- 3\right) x \textcolor{red}{+ 9} = 16 \textcolor{red}{+ 9}$

$\Rightarrow {\left(x - 3\right)}^{2} = 25$

$\textcolor{b l u e}{\text{take the square root of both sides}}$

$x - 3 = \pm 5 \leftarrow \text{ note plus or minus}$

$\Rightarrow x = 3 \pm 5$

$\Rightarrow x = 3 - 5 \text{ or } x = 3 + 5$

$\Rightarrow x = - 2 \text{ or } x = 8$