Solve 2sqrt{x}=x

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

Solve for x

$$x=0$$

$$x=4$$

Solution Steps

Square both sides of the equation.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

Subtract x^{2} from both sides.

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

Factor out x.

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

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

$$x=0 x=4$$

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

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

Simplify. The value x=0 satisfies the equation.

$$0=0$$

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

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

Simplify. The value x=4 satisfies the equation.

$$4=4$$

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

$$x=0 x=4$$