# How do you solve x^2 - 30 = 8x by completing the square?

May 12, 2015

First subtract $8 x$ from both sides to get ${x}^{2} - 8 x - 30 = 0$.

${\left(x - 4\right)}^{2} = {x}^{2} - 8 x + 16$

So:

$0 = {x}^{2} - 8 x - 30$

$= {x}^{2} - 8 x + 16 - 16 - 30$

$= {\left(x - 4\right)}^{2} - 46$

Add 46 to both sides to get

${\left(x - 4\right)}^{2} = 46$

So we have

$x - 4 = \pm \sqrt{46}$

Add 4 to both sides to get

$x = 4 \pm \sqrt{46}$