# How do you solve |x^2 - 4x + 4| =2?

Sep 2, 2016

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

#### Explanation:

Note that ${x}^{2} - 4 x + 4 = {\left(x - 2\right)}^{2}$ which will be non-negative for any Real value of $x$

Hence we find $\left\mid {x}^{2} - 4 x + 4 \right\mid = {\left(x - 2\right)}^{2}$ and our equation becomes:

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

Hence:

$x - 2 = \pm \sqrt{2}$

Add $2$ to both sides to get:

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