Chapter 4 - Quadratic Functions - 4.4 Solving Quadratic Equations by the Square Root Property and Completing the Square - 4.4 Exercises - Page 346: 15

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

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