# How do you solve 2(x-3)^2 = 3?

May 14, 2016

$x = 3 \pm \frac{\sqrt{6}}{2}$

#### Explanation:

Divide both sides by $2$ to get:

${\left(x - 3\right)}^{2} = \frac{3}{2} = \frac{6}{4}$

Take the square root of both ends, allowing either sign:

$x - 3 = \pm \sqrt{\frac{6}{4}} = \pm \frac{\sqrt{6}}{\sqrt{4}} = \pm \frac{\sqrt{6}}{2}$

Add $3$ to both ends to get:

$x = 3 \pm \frac{\sqrt{6}}{2}$