How do you solve using the completing the square method x^2-12x+20=0?

May 29, 2018

$x = 2 \text{ or } x = 10$

Explanation:

$\text{subtract 20 from both sides}$

${x}^{2} - 12 x = - 20$

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

${x}^{2} + 2 \left(- 6\right) x \textcolor{red}{+ 36} = - 20 \textcolor{red}{+ 36}$

${\left(x - 6\right)}^{2} = 16$

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

$\sqrt{{\left(x - 6\right)}^{2}} = \pm \sqrt{16} \leftarrow \textcolor{b l u e}{\text{note plus or minus}}$

$x - 6 = \pm 4$

$\text{add 6 to both sides}$

$x = 6 \pm 4$

$x = 6 - 4 = 2 \text{ or } x = 6 + 4 = 10$