# How do you solve using the completing the square method  x^2-4x=10?

Mar 21, 2016

You take half of the number that's with the single $x$, and add the square of that to both sides.

#### Explanation:

$\to {x}^{2} + 2 \cdot \left(- 2\right) x + {\left(- 2\right)}^{2} = 10 + {\left(- 2\right)}^{2}$

Or, after 'cleaning up':
$\to {\left(x - 2\right)}^{2} = 14$

Then take the square root on both sides (do not forget the negative answer):
$\to x - 2 = \pm \sqrt{14} \to x = 2 + \sqrt{14} \mathmr{and} x = 2 - \sqrt{14}$