Chapter 12.1, Problem 9OE

To determine

To solve: The equation $4x^2=32$ .

Answer to Problem 9OE

The solution set is $\left(2\sqrt{2},-2\sqrt{2}\right)$ .

Explanation of Solution

Given information:

The given expression $4x^2=32$ .

Calculation:

  $\begin{array}{l}\Rightarrow 4x^2=32\\ \Rightarrow \frac{4x^2}{4}=\frac{32}{4}\end{array}$

(Divide by 4 on both sides)

  $\begin{array}{l}\Rightarrow x^2=8\\ \Rightarrow x=\pm \sqrt{8}\\ \Rightarrow x=\pm \sqrt{4\cdot 2}\\ \Rightarrow x=\pm \sqrt{2^2\cdot 2}\\ \Rightarrow x=\pm 2\sqrt{2}\end{array}$

Therefore, the solution set is $\left(2\sqrt{2},-2\sqrt{2}\right)$