#### Answer

The solution set is $\left\{2-3\sqrt3, 2+3\sqrt3\right\}$.

#### Work Step by Step

Get the square root of both sides:
$\sqrt{(x-2)^2} \pm \sqrt{27}
\\x-2 = \pm \sqrt{9(3)}
\\x-2 = \pm 3\sqrt{3}$
Add 2 to both sides:
$x-2+2 = 2 \pm 3\sqrt{3}
\\x=2 \pm 3\sqrt{3}$