Solve sqrt{4x}-5x=-4x

$$\sqrt { 4 x } - 5 x = - 4 x$$

Solve for x

$$x=4$$

$$x=0$$

Solution Steps

Subtract -5x from both sides of the equation.

$$\sqrt{4x}=-4x+5x$$

Combine -4x and 5x to get x.

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

Square both sides of the equation.

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

Calculate \sqrt{4x} to the power of 2 and get 4x.

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

Subtract x^{2} from both sides.

$$4x-x^{2}=0$$

Factor out x.

$$x\left(4-x\right)=0$$

To find equation solutions, solve x=0 and 4-x=0.

$$x=0 x=4$$

Substitute 0 for x in the equation \sqrt{4x}-5x=-4x.

$$\sqrt{4\times 0}-5\times 0=-4\times 0$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute 4 for x in the equation \sqrt{4x}-5x=-4x.

$$\sqrt{4\times 4}-5\times 4=-4\times 4$$

Simplify. The value x=4 satisfies the equation.

$$-16=-16$$

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

$$x=0 x=4$$