Chapter 12.1, Problem 16WE

To determine

To solve: The equation ${\left(x+6\right)}^2=16$ and express irrational solution in simplest radical form.

Answer to Problem 16WE

The solution set is $\left(-2,-10\right)$ .

Explanation of Solution

Given information:

The given equation ${\left(x+6\right)}^2=16$ .

Calculation:

  $\begin{array}{l}\Rightarrow {\left(x+6\right)}^2=16\\ \Rightarrow x+6=\pm \sqrt{16}\\ \Rightarrow x+6=\pm \sqrt{4^2}\\ \Rightarrow x+6=\pm 4\\ \Rightarrow x+6-6=\pm 4-6\end{array}$

(Subtract 6 from both sides)

  $\begin{array}{l}\Rightarrow x=-6\pm 4\\ \Rightarrow x=-2,x=-10\end{array}$

Therefore, the solution set is $\left(-2,-10\right)$ .