# How do you solve using the completing the square method x^2 - 6x =13?

May 6, 2016

$x = 3 + \sqrt{22}$
$x = 3 - \sqrt{22}$

#### Explanation:

Given -

${x}^{2} - 6 x = 13$
Divide the coefficient of $x$ by 2 and add it to both sides

${x}^{2} - 6 x + {\left(\frac{- 6}{2}\right)}^{2} = 13 + + {\left(\frac{- 6}{2}\right)}^{2}$

You have a perfect square on the left hand side

${x}^{2} - 6 x + 9 = 13 + 9$

Rewrite it as -

${\left(x - 3\right)}^{2} = 22$

Taking square on both sides, we have

$\left(x - 3\right) = \pm \sqrt{22}$

$x = 3 + \sqrt{22}$
$x = 3 - \sqrt{22}$