Q. 321 - Intermediate Algebra

Question

In the following exercises, solve.
$2\sqrt{8r+1}-8=2$

Step-by-Step Solution

Answer

The solution of the given equation is $r=3$.

Step 1. Given information.

The given equation is:

$2\sqrt{8r+1}-8=2$

Step 2. Simplify the equation.

The given equation can be written as:

$\begin{array}{rcl}2\sqrt{8r+1}& =& 2+8\\ 2\sqrt{8r+1}& =& 10\end{array}$

Divide both sides by 2.

$\begin{array}{rcl}\sqrt{8r+1}& =& \frac{10}{2}\\ \sqrt{8r+1}& =& 5\end{array}$

Step 3. Solve the equation.

Take square on both sides.

$\begin{array}{rcl}(\sqrt{8r+1}{)}^2& =& (5{)}^2\\ 8r+1& =& 25\\ 8r& =& 25-1\\ 8r& =& 24\end{array}$

Divide both sides by 8.

$\begin{array}{rcl}\frac{8r}{8}& =& \frac{24}{8}\\ r& =& 3\end{array}$

Step 4. Conclusion.

The solution of the given equation is $r=3$.