How do you solve sqrt(9u-4)=sqrt(7u-20)?

Jan 24, 2018

Answer:

See a solution process below:

Explanation:

First, square both sides of the equation to eliminate the radicals while keeping the equation balanced:

${\left(\sqrt{9 u - 4}\right)}^{2} = {\left(\sqrt{7 u - 20}\right)}^{2}$

$9 u - 4 = 7 u - 20$

Next, add $\textcolor{red}{4}$ and subtract $\textcolor{b l u e}{7 u}$ from each side of the equation to isolate the $u$ term while keeping the equation balanced:

$9 u - \textcolor{b l u e}{7 u} - 4 + \textcolor{red}{4} = 7 u - \textcolor{b l u e}{7 u} - 20 + \textcolor{red}{4}$

$\left(9 - \textcolor{b l u e}{7}\right) u - 0 = 0 - 16$

$2 u = - 16$

Now, divide each side of the equation by $\textcolor{red}{2}$ to solve for $u$ while keeping the equation balanced:

$\frac{2 u}{\textcolor{red}{2}} = - \frac{16}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} u}{\cancel{\textcolor{red}{2}}} = - 8$

$u = - 8$

Jan 24, 2018

See below.

Explanation:

$\sqrt{9 u - 4} = \sqrt{7 u - 20}$

Start by squaring both sides. This will remove the radicals:

${\left(\sqrt{9 u - 4}\right)}^{2} = {\left(\sqrt{7 u - 20}\right)}^{2}$

$9 u - 4 = 7 u - 20$

Collect all terms containing the variable on one side of the equation, and all constant terms on the opposite side:

$9 u - 7 u = - 20 + 4$

Simplify by adding like terms:

$2 u = - 16$

We need to get a $u$ on its own.

Divide both sides by $2$:

$\frac{2 u}{2} = \frac{- 16}{2} \to \frac{\cancel{2} u}{\cancel{2}} = \frac{- \cancel{16} 8}{\cancel{2}} \to \textcolor{b l u e}{u = - 8}$