For this problem, I squared both sides of the equation twice and then wrote it as a quadratic with $4$ as the variable. I then used the quadratic equation on this constant and got $4$ different solutions for $x$. I know some of these are extraneous solutions, but how do I know which values of $x$ will be valid solutions of $\sqrt{5-\sqrt{5-x}} = x$ without having to test the solutions? Thank you.