Chapter 12, Problem 69CLR

To determine

To find: The simplification of the given equation.

Answer to Problem 69CLR

The simplification of the given equation is $r=\frac{7}{4},5$

Explanation of Solution

Given,

The given equation is,

  $\sqrt{3r+1}=2r-6$

Calculation:

Solve the given equation.

  $\sqrt{3r+1}=2r-6$

Square both sides.

  $\begin{array}{l}{\left(\sqrt{3r+1}\right)}^2={\left(2r-6\right)}^2\\ 3r+1=4r^2+36-24r\\ 4r^2+36-24r-3r-1=0\\ 4r^2-27r+35=0\end{array}$

Split the middle term.

  $\begin{array}{l}4r^2-20r-7r+35=0\\ 4r\left(r-5\right)-7\left(r-5\right)=0\\ \left(4r-7\right)\left(r-5\right)=0\\ r=\frac{7}{4},5\end{array}$

Thus, the simplification the given equation is $r=\frac{7}{4},5$