Solve sqrt{v+4}-sqrt{5v+16}=0

$$\sqrt { v + 4 } - \sqrt { 5 v + 16 } = 0$$

Solve for v

$$v=-3$$

Solution Steps

Subtract -\sqrt{5v+16} from both sides of the equation.

$$\sqrt{v+4}=\sqrt{5v+16}$$

Square both sides of the equation.

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

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

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

Calculate \sqrt{5v+16} to the power of 2 and get 5v+16.

$$v+4=5v+16$$

Subtract 5v from both sides.

$$v+4-5v=16$$

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

$$-4v+4=16$$

Subtract 4 from both sides.

$$-4v=16-4$$

Subtract 4 from 16 to get 12.

$$-4v=12$$

Divide both sides by -4.

$$v=\frac{12}{-4}$$

Divide 12 by -4 to get -3.

$$v=-3$$

Substitute -3 for v in the equation \sqrt{v+4}-\sqrt{5v+16}=0.

$$\sqrt{-3+4}-\sqrt{5\left(-3\right)+16}=0$$

Simplify. The value v=-3 satisfies the equation.

$$0=0$$

Equation \sqrt{v+4}=\sqrt{5v+16} has a unique solution.

$$v=-3$$