#### Answer

The solutions are $x=-4\pm\dfrac{3}{2}\sqrt{3}$

#### Work Step by Step

$(2x+8)^{2}=27$
Take the square root of both sides:
$\sqrt{(2x+8)^{2}}=\pm\sqrt{27}$
$2x+8=\pm\sqrt{27}$
Substitute $27$ by $9\cdot3$ and simplify:
$2x+8=\pm\sqrt{9\cdot3}$
$2x+8=\pm3\sqrt{3}$
Solve for $x$:
$2x=-8\pm3\sqrt{3}$
$x=-\dfrac{8}{2}\pm\dfrac{3}{2}\sqrt{3}$
$x=-4\pm\dfrac{3}{2}\sqrt{3}$