Solve sqrt{x^2-x}=x

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

Solve for x

$$x=0$$

Solution Steps

Square both sides of the equation.

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

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

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

Subtract x^{2} from both sides.

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

Combine x^{2} and -x^{2} to get 0.

$$-x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -1 is not equal to 0, x must be equal to 0.

$$x=0$$

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

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

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Equation \sqrt{x^{2}-x}=x has a unique solution.

$$x=0$$