Solve sqrt{x}=4x

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

Solve for x

$$x=0$$

$$x=\frac{1}{16}=0.0625$$

Solution Steps

Square both sides of the equation.

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

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

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

Expand \left(4x\right)^{2}.

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

Calculate 4 to the power of 2 and get 16.

$$x=16x^{2}$$

Subtract 16x^{2} from both sides.

$$x-16x^{2}=0$$

Factor out x.

$$x\left(1-16x\right)=0$$

To find equation solutions, solve x=0 and 1-16x=0.

$$x=0 x=\frac{1}{16}$$

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

$$\sqrt{0}=4\times 0$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute \frac{1}{16} for x in the equation \sqrt{x}=4x.

$$\sqrt{\frac{1}{16}}=4\times \frac{1}{16}$$

Simplify. The value x=\frac{1}{16} satisfies the equation.

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

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

$$x=0 x=\frac{1}{16}$$