n^2+2n-85=0

Solution for n^2+2n-85=0 equation:

Simplifying
n2 + 2n + -85 = 0

Reorder the terms:
-85 + 2n + n2 = 0

Solving
-85 + 2n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '85' to each side of the equation.
-85 + 2n + 85 + n2 = 0 + 85

Reorder the terms:
-85 + 85 + 2n + n2 = 0 + 85

Combine like terms: -85 + 85 = 0
0 + 2n + n2 = 0 + 85
2n + n2 = 0 + 85

Combine like terms: 0 + 85 = 85
2n + n2 = 85

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 = 85 + 1

Reorder the terms:
1 + 2n + n2 = 85 + 1

Combine like terms: 85 + 1 = 86
1 + 2n + n2 = 86

Factor a perfect square on the left side:
(n + 1)(n + 1) = 86

Calculate the square root of the right side: 9.273618495

Break this problem into two subproblems by setting 
(n + 1) equal to 9.273618495 and -9.273618495.

Subproblem 1
n + 1 = 9.273618495

Simplifying
n + 1 = 9.273618495

Reorder the terms:
1 + n = 9.273618495

Solving
1 + n = 9.273618495

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 = 9.273618495 + -1

Combine like terms: 1 + -1 = 0
0 + n = 9.273618495 + -1
n = 9.273618495 + -1

Combine like terms: 9.273618495 + -1 = 8.273618495
n = 8.273618495

Simplifying
n = 8.273618495

Subproblem 2
n + 1 = -9.273618495

Simplifying
n + 1 = -9.273618495

Reorder the terms:
1 + n = -9.273618495

Solving
1 + n = -9.273618495

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 = -9.273618495 + -1

Combine like terms: 1 + -1 = 0
0 + n = -9.273618495 + -1
n = -9.273618495 + -1

Combine like terms: -9.273618495 + -1 = -10.273618495
n = -10.273618495

Simplifying
n = -10.273618495

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {8.273618495, -10.273618495}