Answer
$-2$ and $-1$
Work Step by Step
Step 1. Rewrite the equation as $\sqrt {x+2}=x+2$, take square on both sides to get $x+2=x^2+4x+4$ or $x^2+3x+2=0$
Step 2. Factor the equation to get $(x+1)(x+2)=0$, thus $x=-2$ and $x=-1$
Step 3. Check the solution in the original equation, both solutions fit.