Solve for x
x=0
x=9
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\left(3\sqrt{x}\right)^{2}=x^{2}
Square both sides of the equation.
3^{2}\left(\sqrt{x}\right)^{2}=x^{2}
Expand \left(3\sqrt{x}\right)^{2}.
9\left(\sqrt{x}\right)^{2}=x^{2}
Calculate 3 to the power of 2 and get 9.
9x=x^{2}
Calculate \sqrt{x} to the power of 2 and get x.
9x-x^{2}=0
Subtract x^{2} from both sides.
x\left(9-x\right)=0
Factor out x.
x=0 x=9
To find equation solutions, solve x=0 and 9-x=0.
3\sqrt{0}=0
Substitute 0 for x in the equation 3\sqrt{x}=x.
0=0
Simplify. The value x=0 satisfies the equation.
3\sqrt{9}=9
Substitute 9 for x in the equation 3\sqrt{x}=x.
9=9
Simplify. The value x=9 satisfies the equation.
x=0 x=9
List all solutions of 3\sqrt{x}=x.
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