# How do you solve x^2-6x-11=0 by completing the square?

Aug 13, 2016

$x = 3 \pm 2 \sqrt{5}$

#### Explanation:

Move the constant term to the RHS. Take half the $x$ coefficient. Square it and add to both sides.

${x}^{2} - 6 x + {\left(- 3\right)}^{2} = 11 + {\left(- 3\right)}^{2}$

Can simplify this to

${\left(x - 3\right)}^{2} = 20$

Take square roots of both sides

$x - 3 = \pm \sqrt{20} = \pm 2 \sqrt{5}$

$x = 3 \pm 2 \sqrt{5}$