Solve 10sqrt{9x}=3x

$$10 \sqrt{ 9x } = 3x$$

Solve for x

$$x=100$$

$$x=0$$

Solution Steps

Square both sides of the equation.

$$\left(10\sqrt{9x}\right)^{2}=\left(3x\right)^{2}$$

Expand \left(10\sqrt{9x}\right)^{2}.

$$10^{2}\left(\sqrt{9x}\right)^{2}=\left(3x\right)^{2}$$

Calculate 10 to the power of 2 and get 100.

$$100\left(\sqrt{9x}\right)^{2}=\left(3x\right)^{2}$$

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

$$100\times 9x=\left(3x\right)^{2}$$

Multiply 100 and 9 to get 900.

$$900x=\left(3x\right)^{2}$$

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

$$900x=3^{2}x^{2}$$

Calculate 3 to the power of 2 and get 9.

$$900x=9x^{2}$$

Subtract 9x^{2} from both sides.

$$900x-9x^{2}=0$$

Factor out x.

$$x\left(900-9x\right)=0$$

To find equation solutions, solve x=0 and 900-9x=0.

$$x=0 x=100$$

Substitute 0 for x in the equation 10\sqrt{9x}=3x.

$$10\sqrt{9\times 0}=3\times 0$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute 100 for x in the equation 10\sqrt{9x}=3x.

$$10\sqrt{9\times 100}=3\times 100$$

Simplify. The value x=100 satisfies the equation.

$$300=300$$

List all solutions of 10\sqrt{9x}=3x.

$$x=0 x=100$$