# How do you solve using the completing the square method x^2-2x-13 = 0?

Jan 9, 2018

$x = 1 \pm \sqrt{14}$

#### Explanation:

• " the coefficient of the "x^2" term must be 1 which it is"

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

${x}^{2} - 2 x - 13 = 0$

$\Rightarrow {x}^{2} - 2 x = 13$

$\Rightarrow {x}^{2} + 2 \left(- 1\right) x \textcolor{red}{+ 1} = 13 \textcolor{red}{+ 1}$

$\Rightarrow {\left(x - 1\right)}^{2} = 14$

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

$x - 1 = \pm \sqrt{14} \leftarrow \textcolor{b l u e}{\text{note plus or minus}}$

$\Rightarrow x = 1 \pm \sqrt{14}$