# How do you solve the equation sqrt(7k+2)+2=5?

May 30, 2017

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{2}$ from each side of the equation to isolate the radical while keeping the equation balanced:

$\sqrt{7 k + 2} + 2 - \textcolor{red}{2} = 5 - \textcolor{red}{2}$

$\sqrt{7 k + 2} + 0 = 3$

$\sqrt{7 k + 2} = 3$

Next, square both sides of the equation to eliminate the radical while keeping the equation balanced:

${\left(\sqrt{7 k + 2}\right)}^{2} = {3}^{2}$

$7 k + 2 = 9$

Then, subtract $\textcolor{red}{2}$ from each side of the equation to isolate the $k$ term while keeping the equation balanced:

$7 k + 2 - \textcolor{red}{2} = 9 - \textcolor{red}{2}$

$7 k + 0 = 7$

$7 k = 7$

Now, divide each side of the equation by $\textcolor{red}{7}$ to solve for $k$ while keeping the equation balanced:

$\frac{7 k}{\textcolor{red}{7}} = \frac{7}{\textcolor{red}{7}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} k}{\cancel{\textcolor{red}{7}}} = 1$

$k = 1$