Solve x=64sqrt{x}

$$x=64 \sqrt{ x }$$

Solve for x

$$x=4096$$

$$x=0$$

Solution Steps

Square both sides of the equation.

$$x^{2}=\left(64\sqrt{x}\right)^{2}$$

Expand \left(64\sqrt{x}\right)^{2}.

$$x^{2}=64^{2}\left(\sqrt{x}\right)^{2}$$

Calculate 64 to the power of 2 and get 4096.

$$x^{2}=4096\left(\sqrt{x}\right)^{2}$$

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

$$x^{2}=4096x$$

Subtract 4096x from both sides.

$$x^{2}-4096x=0$$

Factor out x.

$$x\left(x-4096\right)=0$$

To find equation solutions, solve x=0 and x-4096=0.

$$x=0 x=4096$$

Substitute 0 for x in the equation x=64\sqrt{x}.

$$0=64\sqrt{0}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute 4096 for x in the equation x=64\sqrt{x}.

$$4096=64\sqrt{4096}$$

Simplify. The value x=4096 satisfies the equation.

$$4096=4096$$

List all solutions of x=64\sqrt{x}.

$$x=0 x=4096$$