# How do you solve \sqrt { 7u + 6} = \sqrt { 5u + 16}?

Mar 10, 2018

$u = 5$

Refer to the explanation for the process.

#### Explanation:

Solve:

$\sqrt{7 u + 6} = \sqrt{5 u + 16}$

Square both sides.

${\left(\sqrt{7 u + 6}\right)}^{2} = {\left(\sqrt{5 u + 16}\right)}^{2}$

$7 u + 6 = 5 u + 16$

Subtract $5 u$ from both sides.

$7 u - 5 u + 6 = 5 u - 5 u + 16$

Simplify.

$2 u + 6 = 0 + 16$

$2 u + 6 = 16$

Subtract $6$ from both sides.

$2 u + 6 - 6 = 16 - 6$

Simplify.

$2 u + 0 = 10$

$2 u = 10$

Divide both sides by $2$.

$\frac{{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}}^{1} u}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} ^ 1 = {\textcolor{red}{\cancel{\textcolor{b l a c k}{10}}}}^{5} / {\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}}^{1}$

Simplify.

$u = 5$

Mar 10, 2018

$u = 5$

#### Explanation:

$\rightarrow \sqrt{7 u + 6} = \sqrt{5 u + 16}$

$\rightarrow {\left(\sqrt{7 u + 6}\right)}^{2} = {\left(\sqrt{5 u + 16}\right)}^{2}$

$\rightarrow 7 u + 6 = 5 u + 16$

$\rightarrow 2 u = 10$

$\rightarrow u = 5$