Solve x=(3sqrt{x}-2)(sqrt{x})

$$x = ( 3 \sqrt { x } - 2 ) ( \sqrt { x } )$$

Solve for x

$$x=1$$

$$x=0$$

Solution Steps

Use the distributive property to multiply 3\sqrt{x}-2 by \sqrt{x}.

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

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

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

Subtract 3x from both sides.

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

Combine x and -3x to get -2x.

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

Add 2\sqrt{x} to both sides.

$$-2x+2\sqrt{x}=0$$

Subtract -2x from both sides of the equation.

$$2\sqrt{x}=2x$$

Cancel out 2 on both sides.

$$\sqrt{x}=x$$

Square both sides of the equation.

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

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

$$x=x^{2}$$

Subtract x^{2} from both sides.

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

Factor out x.

$$x\left(1-x\right)=0$$

To find equation solutions, solve x=0 and 1-x=0.

$$x=0 x=1$$

Substitute 0 for x in the equation x=\left(3\sqrt{x}-2\right)\sqrt{x}.

$$0=\left(3\sqrt{0}-2\right)\sqrt{0}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute 1 for x in the equation x=\left(3\sqrt{x}-2\right)\sqrt{x}.

$$1=\left(3\sqrt{1}-2\right)\sqrt{1}$$

Simplify. The value x=1 satisfies the equation.

$$1=1$$

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

$$x=0 x=1$$