Solve x=2sqrt{x}

$$x=2 \sqrt{ x }$$

Solve for x

$$x=4$$

$$x=0$$

Solution Steps

Square both sides of the equation.

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

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

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

Calculate 2 to the power of 2 and get 4.

$$x^{2}=4\left(\sqrt{x}\right)^{2}$$

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

$$x^{2}=4x$$

Subtract 4x from both sides.

$$x^{2}-4x=0$$

Factor out x.

$$x\left(x-4\right)=0$$

To find equation solutions, solve x=0 and x-4=0.

$$x=0 x=4$$

Substitute 0 for x in the equation x=2\sqrt{x}.

$$0=2\sqrt{0}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute 4 for x in the equation x=2\sqrt{x}.

$$4=2\sqrt{4}$$

Simplify. The value x=4 satisfies the equation.

$$4=4$$

List all solutions of x=2\sqrt{x}.

$$x=0 x=4$$