n^2-2n-88=0

Solution for n^2-2n-88=0 equation:

Simplifying
n2 + -2n + -88 = 0

Reorder the terms:
-88 + -2n + n2 = 0

Solving
-88 + -2n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '88' to each side of the equation.
-88 + -2n + 88 + n2 = 0 + 88

Reorder the terms:
-88 + 88 + -2n + n2 = 0 + 88

Combine like terms: -88 + 88 = 0
0 + -2n + n2 = 0 + 88
-2n + n2 = 0 + 88

Combine like terms: 0 + 88 = 88
-2n + n2 = 88

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 = 88 + 1

Reorder the terms:
1 + -2n + n2 = 88 + 1

Combine like terms: 88 + 1 = 89
1 + -2n + n2 = 89

Factor a perfect square on the left side:
(n + -1)(n + -1) = 89

Calculate the square root of the right side: 9.433981132

Break this problem into two subproblems by setting 
(n + -1) equal to 9.433981132 and -9.433981132.

Subproblem 1
n + -1 = 9.433981132

Simplifying
n + -1 = 9.433981132

Reorder the terms:
-1 + n = 9.433981132

Solving
-1 + n = 9.433981132

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 = 9.433981132 + 1

Combine like terms: -1 + 1 = 0
0 + n = 9.433981132 + 1
n = 9.433981132 + 1

Combine like terms: 9.433981132 + 1 = 10.433981132
n = 10.433981132

Simplifying
n = 10.433981132

Subproblem 2
n + -1 = -9.433981132

Simplifying
n + -1 = -9.433981132

Reorder the terms:
-1 + n = -9.433981132

Solving
-1 + n = -9.433981132

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 = -9.433981132 + 1

Combine like terms: -1 + 1 = 0
0 + n = -9.433981132 + 1
n = -9.433981132 + 1

Combine like terms: -9.433981132 + 1 = -8.433981132
n = -8.433981132

Simplifying
n = -8.433981132

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {10.433981132, -8.433981132}