Solve 2sqrt{x+4}-sqrt{5x+4}=0

$$2 \sqrt{ x+4 } - \sqrt{ 5x+4 } = 0$$

Solve for x

$$x=12$$

Solution Steps

Subtract -\sqrt{5x+4} from both sides of the equation.

$$2\sqrt{x+4}=\sqrt{5x+4}$$

Square both sides of the equation.

$$\left(2\sqrt{x+4}\right)^{2}=\left(\sqrt{5x+4}\right)^{2}$$

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

$$2^{2}\left(\sqrt{x+4}\right)^{2}=\left(\sqrt{5x+4}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4\left(\sqrt{x+4}\right)^{2}=\left(\sqrt{5x+4}\right)^{2}$$

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

$$4\left(x+4\right)=\left(\sqrt{5x+4}\right)^{2}$$

Use the distributive property to multiply 4 by x+4.

$$4x+16=\left(\sqrt{5x+4}\right)^{2}$$

Calculate \sqrt{5x+4} to the power of 2 and get 5x+4.

$$4x+16=5x+4$$

Subtract 5x from both sides.

$$4x+16-5x=4$$

Combine 4x and -5x to get -x.

$$-x+16=4$$

Subtract 16 from both sides.

$$-x=4-16$$

Subtract 16 from 4 to get -12.

$$-x=-12$$

Multiply both sides by -1.

$$x=12$$

Substitute 12 for x in the equation 2\sqrt{x+4}-\sqrt{5x+4}=0.

$$2\sqrt{12+4}-\sqrt{5\times 12+4}=0$$

Simplify. The value x=12 satisfies the equation.

$$0=0$$

Equation 2\sqrt{x+4}=\sqrt{5x+4} has a unique solution.

$$x=12$$