# How do you solve using the completing the square method x^2- 8x + 12 = 0?

Nov 1, 2017

$x = 2 \text{ or } x = 6$

#### Explanation:

$\text{place the constant term on the right side}$

$\Rightarrow {x}^{2} - 8 x = - 12$

$\text{to use the method of "color(blue)"completing the square}$

• " ensure the coefficient of the "x^2" term is 1"

${x}^{2} - 8 x = - 12 \leftarrow \textcolor{b l u e}{\text{coefficient of 1}}$

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

${x}^{2} + 2 \left(- 4\right) x \textcolor{red}{+ 16} = - 12 \textcolor{red}{+ 16}$

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

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

$\Rightarrow x - 4 = \pm \sqrt{4} \leftarrow \textcolor{b l u e}{\text{note plus or minus}}$

$\Rightarrow x = 4 \pm 2$

$\Rightarrow x = 4 + 2 = 6 \text{ or } x = 4 - 2 = 2$