Chapter 12, Problem 2CT

To determine

To calculate: The value of $a$ from the following expression $3{\left(a-5\right)}^2=21$ .

Answer to Problem 2CT

The value of the $a$ is $\pm \sqrt{7}+5$ .

Explanation of Solution

Given information:

The expression is given as:

  $3{\left(a-5\right)}^2=21$

Calculation:

Consider the expression,

  $3{\left(a-5\right)}^2=21$

Divided by 3 on the both side of equation,

  $\begin{array}{c}\frac{3{\left(a-5\right)}^2}{3}=\frac{21}{3}\\ {\left(a-5\right)}^2=7\end{array}$

Take the root on both side of equation,

  $\sqrt{{\left(a-5\right)}^2}=\pm \sqrt{7}$

Furthermore,

  $\begin{array}{c}\left(a-5\right)=\pm \sqrt{7}\\ a=\pm \sqrt{7}+5\end{array}$

Thus, the value of the $a$ is $\pm \sqrt{7}+5$ .