Answer
$$x=\frac{19-\sqrt{37}}{2}$$
Work Step by Step
Using the rules of Algebra to solve the equation, we find:
$$\left(\sqrt{x+\sqrt{x}}\right)^2=3^2 \\ x+\sqrt{x}=9 \\ \left(\sqrt{x}\right)^2=\left(9-x\right)^2 \\ x=81-18x+x^2 \\ x=\frac{19-\sqrt{37}}{2}$$
