n^2+16n-7=0

Solution for n^2+16n-7=0 equation:

Simplifying
n2 + 16n + -7 = 0

Reorder the terms:
-7 + 16n + n2 = 0

Solving
-7 + 16n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 16n + 7 + n2 = 0 + 7

Reorder the terms:
-7 + 7 + 16n + n2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 16n + n2 = 0 + 7
16n + n2 = 0 + 7

Combine like terms: 0 + 7 = 7
16n + n2 = 7

The n term is 16n.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16n + 64 + n2 = 7 + 64

Reorder the terms:
64 + 16n + n2 = 7 + 64

Combine like terms: 7 + 64 = 71
64 + 16n + n2 = 71

Factor a perfect square on the left side:
(n + 8)(n + 8) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(n + 8) equal to 8.426149773 and -8.426149773.

Subproblem 1
n + 8 = 8.426149773

Simplifying
n + 8 = 8.426149773

Reorder the terms:
8 + n = 8.426149773

Solving
8 + n = 8.426149773

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + n = 8.426149773 + -8

Combine like terms: 8 + -8 = 0
0 + n = 8.426149773 + -8
n = 8.426149773 + -8

Combine like terms: 8.426149773 + -8 = 0.426149773
n = 0.426149773

Simplifying
n = 0.426149773

Subproblem 2
n + 8 = -8.426149773

Simplifying
n + 8 = -8.426149773

Reorder the terms:
8 + n = -8.426149773

Solving
8 + n = -8.426149773

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + n = -8.426149773 + -8

Combine like terms: 8 + -8 = 0
0 + n = -8.426149773 + -8
n = -8.426149773 + -8

Combine like terms: -8.426149773 + -8 = -16.426149773
n = -16.426149773

Simplifying
n = -16.426149773

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.426149773, -16.426149773}