Checking my answer

Sqrt(x)=-x

x=0

Right? It can't be positive or negative so it has to be 0.

looks good.

You could arrange as:

$\displaystyle x+\sqrt{x}=0$

$\displaystyle \sqrt{x}(\sqrt{x}+1)=0$

Since $\displaystyle 0\le\sqrt{x}$ we must have:

$\displaystyle \sqrt{x}=0$

$\displaystyle x=0$