#### Answer

$x=-4-\sqrt {22},-4+\sqrt {22}$

#### Work Step by Step

When taking the square root of a number, you get a positive and a negative answer.
$-0.5(x+4)^2-9=-20$
$-0.5(x+4)^2=-11$
$(x+4)^2=22$
$x+4=\sqrt {22}$
$x=-4+\sqrt {22}$
or
$x+4=-\sqrt {22}$
$x=-4-\sqrt {22}$.
So
$x=-4-\sqrt {22},-4+\sqrt {22}$.