Answer
$x=\frac{-8-3\sqrt3}{2},\frac{-8+3\sqrt3}{2}$
Work Step by Step
$(2x+8)^{2}=27$
$2x+8=\sqrt 27$
$2x+8=-\sqrt 27$
$x=\frac{-8-3\sqrt3}{2},\frac{-8+3\sqrt3}{2}$
Take the square root of both sides. Then isolate $x$ from both of the resulting equations to get two answers.