Chapter 9, Problem 1MCP

In Exercises 1-12, solve each equation by the method of your choice Simplify irrational solutions, if possible.

1. ${\left(3x-2\right)}^2=100$

To determine

To solve:

The given equation. Simplify irrational solutions.

Answer to Problem 1MCP

The solutions for our given equation are $x=-\frac{8}{3}\text{, }x=4$.

Explanation of Solution

Given:

An equation: ${(3x-2)}^2=100$.

Calculation:

To solve our equation, we will take square root of both sides of the given equation as shown below:

   $\begin{array}{l}$ {(3x-2)}^2=100\text{(Given equation)}$\sqrt{{(3x-2)}^2}=\pm \sqrt{100}(\text{Taking square root of both sides)}\\ 3x-2=\pm \sqrt{100}(\text{Using radical rule }\sqrt[n]{a^n}=a)\\ 3x-2=\pm \sqrt{{10}^2}({\text{Writing 100 as 10}}^2)\\ 3x-2=\pm 10(\text{Using radical rule }\sqrt[n]{a^n}=a)\\ 3x-2=-10\text{ (or) }3x-2=10\\ 3x=-8\text{ (or) }3x=12(\text{Adding 2 on each side)}\\ \frac{3x}{3}=-\frac{8}{3}\text{ (or) }\frac{3x}{3}=\frac{12}{3}(\text{Dividing each sides by 3)}\\ x=-\frac{8}{3}\text{ (or) }x=4\\ \end{array}$

Therefore, the solutions for our given equation are $x=-\frac{8}{3}\text{, }x=4$.