Solve 3x-2sqrt{9x}=0

$$3 x - 2 \sqrt { 9 x } = 0$$

Solve for x

$$x=4$$

$$x=0$$

Solution Steps

Subtract 3x from both sides of the equation.

$$-2\sqrt{9x}=-3x$$

Square both sides of the equation.

$$\left(-2\sqrt{9x}\right)^{2}=\left(-3x\right)^{2}$$

Expand \left(-2\sqrt{9x}\right)^{2}.

$$\left(-2\right)^{2}\left(\sqrt{9x}\right)^{2}=\left(-3x\right)^{2}$$

Calculate -2 to the power of 2 and get 4.

$$4\left(\sqrt{9x}\right)^{2}=\left(-3x\right)^{2}$$

Calculate \sqrt{9x} to the power of 2 and get 9x.

$$4\times 9x=\left(-3x\right)^{2}$$

Multiply 4 and 9 to get 36.

$$36x=\left(-3x\right)^{2}$$

Expand \left(-3x\right)^{2}.

$$36x=\left(-3\right)^{2}x^{2}$$

Calculate -3 to the power of 2 and get 9.

$$36x=9x^{2}$$

Subtract 9x^{2} from both sides.

$$36x-9x^{2}=0$$

Factor out x.

$$x\left(36-9x\right)=0$$

To find equation solutions, solve x=0 and 36-9x=0.

$$x=0 x=4$$

Substitute 0 for x in the equation 3x-2\sqrt{9x}=0.

$$3\times 0-2\sqrt{9\times 0}=0$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute 4 for x in the equation 3x-2\sqrt{9x}=0.

$$3\times 4-2\sqrt{9\times 4}=0$$

Simplify. The value x=4 satisfies the equation.

$$0=0$$

List all solutions of -2\sqrt{9x}=-3x.

$$x=0 x=4$$