Solve x-sqrt{x^2-2x}=0

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

Solve for x

$$x=0$$

Solution Steps

Subtract x from both sides of the equation.

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

Cancel out -1 on both sides.

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

Square both sides of the equation.

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

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

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

Subtract x^{2} from both sides.

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

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

$$-2x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -2 is not equal to 0, x must be equal to 0.

$$x=0$$

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

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

Simplify. The value x=0 satisfies the equation.

$$0=0$$

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

$$x=0$$