Solve 1/2sqrt{x}=x

$$\frac { 1 } { 2 } \sqrt { x } = x$$

Solve for x

$$x=0$$

$$x=\frac{1}{4}=0.25$$

Solution Steps

Square both sides of the equation.

$$\left(\frac{1}{2}\sqrt{x}\right)^{2}=x^{2}$$

Expand \left(\frac{1}{2}\sqrt{x}\right)^{2}.

$$\left(\frac{1}{2}\right)^{2}\left(\sqrt{x}\right)^{2}=x^{2}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{1}{4}\left(\sqrt{x}\right)^{2}=x^{2}$$

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

$$\frac{1}{4}x=x^{2}$$

Subtract x^{2} from both sides.

$$\frac{1}{4}x-x^{2}=0$$

Factor out x.

$$x\left(\frac{1}{4}-x\right)=0$$

To find equation solutions, solve x=0 and \frac{1}{4}-x=0.

$$x=0 x=\frac{1}{4}$$

Substitute 0 for x in the equation \frac{1}{2}\sqrt{x}=x.

$$\frac{1}{2}\sqrt{0}=0$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute \frac{1}{4} for x in the equation \frac{1}{2}\sqrt{x}=x.

$$\frac{1}{2}\sqrt{\frac{1}{4}}=\frac{1}{4}$$

Simplify. The value x=\frac{1}{4} satisfies the equation.

$$\frac{1}{4}=\frac{1}{4}$$

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

$$x=0 x=\frac{1}{4}$$