Step 1
Given;
[tex]n^2+16n+82=10[/tex]
Required to solve the problem using completing the square method
Step 2
Move 10 to the left.
[tex]n^2+16n+82-10=0[/tex]
Simplify
[tex]n^2+16n+72=0[/tex]
Step 3
Add 64 and subtract 64
[tex]n^2+16n+72=n^2+16n+72+64-64[/tex]
Step 4
Complete the square
[tex]8+(n^2+16n+64)=\text{ }8+(n+8)^2[/tex]
Step 5
Find the value of n
[tex]\begin{gathered} 8+(n+8)^2=0 \\ (n+8)^2=-8 \\ n+8=\pm\sqrt[]{-8} \\ \end{gathered}[/tex][tex]\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}[/tex]
Hence,
n= -8+(2√2)i
or
n= -8-(2√2)i
