n(n+2)=118

Solution for n(n+2)=118 equation:

Simplifying
n(n + 2) = 118

Reorder the terms:
n(2 + n) = 118
(2 * n + n * n) = 118
(2n + n2) = 118

Solving
2n + n2 = 118

Solving for variable 'n'.

Reorder the terms:
-118 + 2n + n2 = 118 + -118

Combine like terms: 118 + -118 = 0
-118 + 2n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '118' to each side of the equation.
-118 + 2n + 118 + n2 = 0 + 118

Reorder the terms:
-118 + 118 + 2n + n2 = 0 + 118

Combine like terms: -118 + 118 = 0
0 + 2n + n2 = 0 + 118
2n + n2 = 0 + 118

Combine like terms: 0 + 118 = 118
2n + n2 = 118

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 = 118 + 1

Reorder the terms:
1 + 2n + n2 = 118 + 1

Combine like terms: 118 + 1 = 119
1 + 2n + n2 = 119

Factor a perfect square on the left side:
(n + 1)(n + 1) = 119

Calculate the square root of the right side: 10.908712115

Break this problem into two subproblems by setting 
(n + 1) equal to 10.908712115 and -10.908712115.

Subproblem 1
n + 1 = 10.908712115

Simplifying
n + 1 = 10.908712115

Reorder the terms:
1 + n = 10.908712115

Solving
1 + n = 10.908712115

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 = 10.908712115 + -1

Combine like terms: 1 + -1 = 0
0 + n = 10.908712115 + -1
n = 10.908712115 + -1

Combine like terms: 10.908712115 + -1 = 9.908712115
n = 9.908712115

Simplifying
n = 9.908712115

Subproblem 2
n + 1 = -10.908712115

Simplifying
n + 1 = -10.908712115

Reorder the terms:
1 + n = -10.908712115

Solving
1 + n = -10.908712115

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 = -10.908712115 + -1

Combine like terms: 1 + -1 = 0
0 + n = -10.908712115 + -1
n = -10.908712115 + -1

Combine like terms: -10.908712115 + -1 = -11.908712115
n = -11.908712115

Simplifying
n = -11.908712115

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {9.908712115, -11.908712115}