Solve 2sqrt{x}=x/4

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

Solve for x

$$x=0$$

$$x=64$$

Solution Steps

Square both sides of the equation.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

To raise \frac{x}{4} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 4 to the power of 2 and get 16.

$$4x=\frac{x^{2}}{16}$$

Multiply both sides of the equation by 16.

$$64x=x^{2}$$

Subtract x^{2} from both sides.

$$64x-x^{2}=0$$

Factor out x.

$$x\left(64-x\right)=0$$

To find equation solutions, solve x=0 and 64-x=0.

$$x=0 x=64$$

Substitute 0 for x in the equation 2\sqrt{x}=\frac{x}{4}.

$$2\sqrt{0}=\frac{0}{4}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute 64 for x in the equation 2\sqrt{x}=\frac{x}{4}.

$$2\sqrt{64}=\frac{64}{4}$$

Simplify. The value x=64 satisfies the equation.

$$16=16$$

List all solutions of 2\sqrt{x}=\frac{x}{4}.

$$x=0 x=64$$