Solve 6x+12sqrt{x}=0

$$6 x + 12 \sqrt { x } = 0$$

Solve for x

$$x=0$$

Solution Steps

Subtract 6x from both sides of the equation.

$$12\sqrt{x}=-6x$$

Square both sides of the equation.

$$\left(12\sqrt{x}\right)^{2}=\left(-6x\right)^{2}$$

Expand \left(12\sqrt{x}\right)^{2}.

$$12^{2}\left(\sqrt{x}\right)^{2}=\left(-6x\right)^{2}$$

Calculate 12 to the power of 2 and get 144.

$$144\left(\sqrt{x}\right)^{2}=\left(-6x\right)^{2}$$

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

$$144x=\left(-6x\right)^{2}$$

Expand \left(-6x\right)^{2}.

$$144x=\left(-6\right)^{2}x^{2}$$

Calculate -6 to the power of 2 and get 36.

$$144x=36x^{2}$$

Subtract 36x^{2} from both sides.

$$144x-36x^{2}=0$$

Factor out x.

$$x\left(144-36x\right)=0$$

To find equation solutions, solve x=0 and 144-36x=0.

$$x=0 x=4$$

Substitute 0 for x in the equation 6x+12\sqrt{x}=0.

$$6\times 0+12\sqrt{0}=0$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute 4 for x in the equation 6x+12\sqrt{x}=0.

$$6\times 4+12\sqrt{4}=0$$

Simplify. The value x=4 does not satisfy the equation.

$$48=0$$

Equation 12\sqrt{x}=-6x has a unique solution.

$$x=0$$