Solve sqrt{x}=-x

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

Solve for x

$$x=0$$

Solution Steps

Square both sides of the equation.

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

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

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

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

$$x=x^{2}$$

Subtract x^{2} from both sides.

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

Factor out x.

$$x\left(1-x\right)=0$$

To find equation solutions, solve x=0 and 1-x=0.

$$x=0 x=1$$

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

$$\sqrt{0}=0$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute 1 for x in the equation \sqrt{x}=-x.

$$\sqrt{1}=-1$$

Simplify. The value x=1 does not satisfy the equation because the left and the right hand side have opposite signs.

$$1=-1$$

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

$$x=0$$