n^2+2n-169=0

Solution for n^2+2n-169=0 equation:

Simplifying
n2 + 2n + -169 = 0

Reorder the terms:
-169 + 2n + n2 = 0

Solving
-169 + 2n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '169' to each side of the equation.
-169 + 2n + 169 + n2 = 0 + 169

Reorder the terms:
-169 + 169 + 2n + n2 = 0 + 169

Combine like terms: -169 + 169 = 0
0 + 2n + n2 = 0 + 169
2n + n2 = 0 + 169

Combine like terms: 0 + 169 = 169
2n + n2 = 169

The n term is 2n.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2n + 1 + n2 = 169 + 1

Reorder the terms:
1 + 2n + n2 = 169 + 1

Combine like terms: 169 + 1 = 170
1 + 2n + n2 = 170

Factor a perfect square on the left side:
(n + 1)(n + 1) = 170

Calculate the square root of the right side: 13.03840481

Break this problem into two subproblems by setting 
(n + 1) equal to 13.03840481 and -13.03840481.

Subproblem 1
n + 1 = 13.03840481

Simplifying
n + 1 = 13.03840481

Reorder the terms:
1 + n = 13.03840481

Solving
1 + n = 13.03840481

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = 13.03840481 + -1

Combine like terms: 1 + -1 = 0
0 + n = 13.03840481 + -1
n = 13.03840481 + -1

Combine like terms: 13.03840481 + -1 = 12.03840481
n = 12.03840481

Simplifying
n = 12.03840481

Subproblem 2
n + 1 = -13.03840481

Simplifying
n + 1 = -13.03840481

Reorder the terms:
1 + n = -13.03840481

Solving
1 + n = -13.03840481

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = -13.03840481 + -1

Combine like terms: 1 + -1 = 0
0 + n = -13.03840481 + -1
n = -13.03840481 + -1

Combine like terms: -13.03840481 + -1 = -14.03840481
n = -14.03840481

Simplifying
n = -14.03840481

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {12.03840481, -14.03840481}