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\sqrt{5v+16}=\sqrt{7v+6}
Subtract -\sqrt{7v+6} from both sides of the equation.
\left(\sqrt{5v+16}\right)^{2}=\left(\sqrt{7v+6}\right)^{2}
Square both sides of the equation.
5v+16=\left(\sqrt{7v+6}\right)^{2}
Calculate \sqrt{5v+16} to the power of 2 and get 5v+16.
5v+16=7v+6
Calculate \sqrt{7v+6} to the power of 2 and get 7v+6.
5v+16-7v=6
Subtract 7v from both sides.
-2v+16=6
Combine 5v and -7v to get -2v.
-2v=6-16
Subtract 16 from both sides.
-2v=-10
Subtract 16 from 6 to get -10.
v=\frac{-10}{-2}
Divide both sides by -2.
v=5
Divide -10 by -2 to get 5.
\sqrt{5\times 5+16}-\sqrt{7\times 5+6}=0
Substitute 5 for v in the equation \sqrt{5v+16}-\sqrt{7v+6}=0.
0=0
Simplify. The value v=5 satisfies the equation.
v=5
Equation \sqrt{5v+16}=\sqrt{7v+6} has a unique solution.