Solve sqrt{x+x}=x

$$\sqrt { x + x } = x$$

Solve for x

$$x=2$$

$$x=0$$

Solution Steps

Square both sides of the equation.

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

Combine x and x to get 2x.

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

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

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

Subtract x^{2} from both sides.

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

Factor out x.

$$x\left(2-x\right)=0$$

To find equation solutions, solve x=0 and 2-x=0.

$$x=0 x=2$$

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

$$\sqrt{0+0}=0$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

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

$$\sqrt{2+2}=2$$

Simplify. The value x=2 satisfies the equation.

$$2=2$$

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

$$x=0 x=2$$