Sqrt(x)=-x x=0 Right? It can't be positive or negative so it has to be 0.
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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: $\displaystyle \sqrt{x}=0$ $\displaystyle x=0$
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