Chapter 12.1, Problem 46WE

To determine

To solve: The equation $3{\left(5x-2\right)}^2=27$ .

Answer to Problem 46WE

The solution set is $\left(1,-\frac{1}{5}\right)$ .

Explanation of Solution

Given information:

The given equation $3{\left(5x-2\right)}^2=27$ .

Calculation:

  $\begin{array}{l}\Rightarrow 3{\left(5x-2\right)}^2=27\\ \Rightarrow \frac{3{\left(5x-2\right)}^2}{3}=\frac{27}{3}\end{array}$

(Divide by 3 on both sides)

  $\begin{array}{l}\Rightarrow {\left(5x-2\right)}^2=9\\ \Rightarrow 5x-2=\pm \sqrt{9}\\ \Rightarrow 5x-2=\pm \sqrt{3^2}\\ \Rightarrow 5x-2=\pm 3\\ \Rightarrow 5x-2+2=\pm 3+2\end{array}$

(Adding 2 on both sides)

  $\begin{array}{l}\Rightarrow 5x=\pm 3+2\\ \Rightarrow \frac{5x}{5}=\frac{\pm 3+2}{5}\end{array}$

(Divide by 5 on both sides)

  $\begin{array}{l}\Rightarrow x=\frac{\pm 3+2}{5}\\ \Rightarrow x=1;x=-\frac{1}{5}\end{array}$

Therefore, the solution set is $\left(1,-\frac{1}{5}\right)$ .