# How do you solve the equation x^2-8x+11=0 by completing the square?

Dec 5, 2016

$x = 4 + \sqrt{5}$ and
$x = 4 - \sqrt{5}$

#### Explanation:

${x}^{2} - 2 \left(x\right) \left(4\right) + {\left(4\right)}^{2} - {\left(4\right)}^{2} + 11$ add and subtract ${\left(4\right)}^{2}$
${\left(x - 4\right)}^{2} - 5 = 0$
${\left(x - 4\right)}^{2} = 5$
taking sq root both sides$\sqrt{{\left(x - 4\right)}^{2}} = \sqrt{5}$
$x - 4 = \pm \sqrt{5}$
$x = 4 \pm \sqrt{5}$

Therefore
$x = 4 + \sqrt{5}$ and
$x = 4 - \sqrt{5}$