Solve sqrt{x}+4x=0

$$\sqrt { x } + 4 x = 0$$

Solve for x

$$x=0$$

Solution Steps

Subtract 4x from both sides of the equation.

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

Square both sides of the equation.

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

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

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

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

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

Calculate -4 to the power of 2 and get 16.

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

Subtract 16x^{2} from both sides.

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

Factor out x.

$$x\left(1-16x\right)=0$$

To find equation solutions, solve x=0 and 1-16x=0.

$$x=0 x=\frac{1}{16}$$

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

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

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute \frac{1}{16} for x in the equation \sqrt{x}+4x=0.

$$\sqrt{\frac{1}{16}}+4\times \frac{1}{16}=0$$

Simplify. The value x=\frac{1}{16} does not satisfy the equation.

$$\frac{1}{2}=0$$

Equation \sqrt{x}=-4x has a unique solution.

$$x=0$$