Solve 12sqrt{x}=4x

$$12 \sqrt { x } = 4 x$$

Solve for x

$$x=0$$

$$x=9$$

Solution Steps

Square both sides of the equation.

$$\left(12\sqrt{x}\right)^{2}=\left(4x\right)^{2}$$

Expand \left(12\sqrt{x}\right)^{2}.

$$12^{2}\left(\sqrt{x}\right)^{2}=\left(4x\right)^{2}$$

Calculate 12 to the power of 2 and get 144.

$$144\left(\sqrt{x}\right)^{2}=\left(4x\right)^{2}$$

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

$$144x=\left(4x\right)^{2}$$

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

$$144x=4^{2}x^{2}$$

Calculate 4 to the power of 2 and get 16.

$$144x=16x^{2}$$

Subtract 16x^{2} from both sides.

$$144x-16x^{2}=0$$

Factor out x.

$$x\left(144-16x\right)=0$$

To find equation solutions, solve x=0 and 144-16x=0.

$$x=0 x=9$$

Substitute 0 for x in the equation 12\sqrt{x}=4x.

$$12\sqrt{0}=4\times 0$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute 9 for x in the equation 12\sqrt{x}=4x.

$$12\sqrt{9}=4\times 9$$

Simplify. The value x=9 satisfies the equation.

$$36=36$$

List all solutions of 12\sqrt{x}=4x.

$$x=0 x=9$$