Solve x=sqrt{2x^2}

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

Solve for x

$$x=0$$

Solution Steps

Square both sides of the equation.

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

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

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

Subtract 2x^{2} from both sides.

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

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

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

Divide both sides by -1. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

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

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

Simplify. The value x=0 satisfies the equation.

$$0=0$$

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

$$x=0$$