Solve 16sqrt{x}=8x

$$16 \sqrt { x } = 8 x$$

Solve for x

$$x=0$$

$$x=4$$

Solution Steps

Square both sides of the equation.

$$\left(16\sqrt{x}\right)^{2}=\left(8x\right)^{2}$$

Expand \left(16\sqrt{x}\right)^{2}.

$$16^{2}\left(\sqrt{x}\right)^{2}=\left(8x\right)^{2}$$

Calculate 16 to the power of 2 and get 256.

$$256\left(\sqrt{x}\right)^{2}=\left(8x\right)^{2}$$

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

$$256x=\left(8x\right)^{2}$$

Expand \left(8x\right)^{2}.

$$256x=8^{2}x^{2}$$

Calculate 8 to the power of 2 and get 64.

$$256x=64x^{2}$$

Subtract 64x^{2} from both sides.

$$256x-64x^{2}=0$$

Factor out x.

$$x\left(256-64x\right)=0$$

To find equation solutions, solve x=0 and 256-64x=0.

$$x=0 x=4$$

Substitute 0 for x in the equation 16\sqrt{x}=8x.

$$16\sqrt{0}=8\times 0$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute 4 for x in the equation 16\sqrt{x}=8x.

$$16\sqrt{4}=8\times 4$$

Simplify. The value x=4 satisfies the equation.

$$32=32$$

List all solutions of 16\sqrt{x}=8x.

$$x=0 x=4$$