Solve sqrt{4v+7}=sqrt{6v-15}

$$\sqrt { 4 v + 7 } = \sqrt { 6 v - 15 }$$

Solve for v

$$v=11$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{4v+7}\right)^{2}=\left(\sqrt{6v-15}\right)^{2}$$

Calculate \sqrt{4v+7} to the power of 2 and get 4v+7.

$$4v+7=\left(\sqrt{6v-15}\right)^{2}$$

Calculate \sqrt{6v-15} to the power of 2 and get 6v-15.

$$4v+7=6v-15$$

Subtract 6v from both sides.

$$4v+7-6v=-15$$

Combine 4v and -6v to get -2v.

$$-2v+7=-15$$

Subtract 7 from both sides.

$$-2v=-15-7$$

Subtract 7 from -15 to get -22.

$$-2v=-22$$

Divide both sides by -2.

$$v=\frac{-22}{-2}$$

Divide -22 by -2 to get 11.

$$v=11$$

Substitute 11 for v in the equation \sqrt{4v+7}=\sqrt{6v-15}.

$$\sqrt{4\times 11+7}=\sqrt{6\times 11-15}$$

Simplify. The value v=11 satisfies the equation.

$$51^{\frac{1}{2}}=51^{\frac{1}{2}}$$

Equation \sqrt{4v+7}=\sqrt{6v-15} has a unique solution.

$$v=11$$