Solve sqrt{2x}=xsqrt{2}

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

Solve for x

$$x=0$$

$$x=1$$

Solution Steps

Square both sides of the equation.

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

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

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

Expand \left(x\sqrt{2}\right)^{2}.

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

The square of \sqrt{2} is 2.

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

Cancel out 2 on both sides.

$$x=x^{2}$$

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{2x}=x\sqrt{2}.

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

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute 1 for x in the equation \sqrt{2x}=x\sqrt{2}.

$$\sqrt{2\times 1}=1\sqrt{2}$$

Simplify. The value x=1 satisfies the equation.

$$2^{\frac{1}{2}}=2^{\frac{1}{2}}$$

List all solutions of \sqrt{2x}=\sqrt{2}x.

$$x=0 x=1$$