Solve x=3sqrt{x}

$$x = 3 \sqrt { x }$$

Solve for x

$$x=9$$

$$x=0$$

Solution Steps

Square both sides of the equation.

$$x^{2}=\left(3\sqrt{x}\right)^{2}$$

Expand \left(3\sqrt{x}\right)^{2}.

$$x^{2}=3^{2}\left(\sqrt{x}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}=9\left(\sqrt{x}\right)^{2}$$

Calculate \sqrt{x} to the power of 2 and get x.

$$x^{2}=9x$$

Subtract 9x from both sides.

$$x^{2}-9x=0$$

Factor out x.

$$x\left(x-9\right)=0$$

To find equation solutions, solve x=0 and x-9=0.

$$x=0 x=9$$

Substitute 0 for x in the equation x=3\sqrt{x}.

$$0=3\sqrt{0}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute 9 for x in the equation x=3\sqrt{x}.

$$9=3\sqrt{9}$$

Simplify. The value x=9 satisfies the equation.

$$9=9$$

List all solutions of x=3\sqrt{x}.

$$x=0 x=9$$