Solve sqrt{0-x}=x

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

Solve for x

$$x=0$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{0-x}\right)^{2}=x^{2}$$

Anything plus zero gives itself.

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

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

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

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{0-x}=x.

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

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute -1 for x in the equation \sqrt{0-x}=x.

$$\sqrt{0-\left(-1\right)}=-1$$

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.

$$x=0$$