Chapter 11, Problem 1MCP

To determine

To Calculate:

The value of the given equation and simplify the solutions if possible.

Answer to Problem 1MCP

Solution:

The solution set is $\left\{\frac{11}{3},-\frac{1}{3}\right\}$ .

Given:

The given equation is ${\left(3x-5\right)}^2=36$ .

Explanation of Solution

Calculation:

Applying the square root in the given equation, we get

  $\begin{array}{c}\left(3x-5\right)=\pm \sqrt{36}\\ 3x-5=\pm 6\end{array}$

Now, write the two equations separately.

  $3x-5=6\text{ or }3x-5=-6$

Now, solve for x.

  $\begin{array}{l}3x=11\text{ or }3x=-1\\ x=\frac{11}{3}\text{ or }x=-\frac{1}{3}\end{array}$

Thus, there are two possible solutions: $\left\{\frac{11}{3},-\frac{1}{3}\right\}$