Q. 26 - Intermediate Algebra

Question

In the following exercises, solve each equation.

${(n+5)}^2=32$

Step-by-Step Solution

Answer

The solution of the equation is $n=-5+4\sqrt{2,}-5-4\sqrt{2}$

Step 1. Given information

In the given question we have to solve given equation. 

${(n+5)}^2=32$

Step 2. The given equation is ( n + 5 ) 2 = 32

Use the Square Root Property.

$n+5=\pm \sqrt{32}$

Step 3. Simplify the radical.

$$\begin{gathered} n+5=\pm \sqrt{2\times 16} \\ n+5=\pm 4\sqrt{2} \end{gathered}$$

Subtract 5 on both side

$$\begin{gathered} n+5-5=-5\pm 4\sqrt{2} \\ n=-5\pm 4\sqrt{2} \end{gathered}$$

Step 4. Solve for n

$n=-5+4\sqrt{2} n=-5-4\sqrt{2}$