Question

Need help with number three

Answer 1

Step 1

Given;

`n^2+16n+82=10`

Required to solve the problem using completing the square method

Step 2

Move 10 to the left.

`n^2+16n+82-10=0`

Simplify

`n^2+16n+72=0`

Step 3

Add 64 and subtract 64

`n^2+16n+72=n^2+16n+72+64-64`

Step 4

Complete the square

`8+(n^2+16n+64)=\text{ }8+(n+8)^2`

Step 5

Find the value of n

`\begin{gathered} 8+(n+8)^2=0 \\ (n+8)^2=-8 \\ n+8=\pm\sqrt[]{-8} \\ \end{gathered}`
`\begin{gathered} n=\text{ -8}\pm\sqrt[]{-8} \\ n=-8\pm\sqrt[]{8}i \\ n=-8\pm2\sqrt[]{2}i \\ n=-8+(2\sqrt[]{2})i \\ or \\ n=-8-(2\sqrt[]{2})i \end{gathered}`

Hence,

n= -8+(2√2)i

or

n= -8-(2√2)i