h^2+2h=108

Solution for h^2+2h=108 equation:

Simplifying
h2 + 2h = 108

Reorder the terms:
2h + h2 = 108

Solving
2h + h2 = 108

Solving for variable 'h'.

Reorder the terms:
-108 + 2h + h2 = 108 + -108

Combine like terms: 108 + -108 = 0
-108 + 2h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '108' to each side of the equation.
-108 + 2h + 108 + h2 = 0 + 108

Reorder the terms:
-108 + 108 + 2h + h2 = 0 + 108

Combine like terms: -108 + 108 = 0
0 + 2h + h2 = 0 + 108
2h + h2 = 0 + 108

Combine like terms: 0 + 108 = 108
2h + h2 = 108

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

Add '1' to each side of the equation.
2h + 1 + h2 = 108 + 1

Reorder the terms:
1 + 2h + h2 = 108 + 1

Combine like terms: 108 + 1 = 109
1 + 2h + h2 = 109

Factor a perfect square on the left side:
(h + 1)(h + 1) = 109

Calculate the square root of the right side: 10.440306509

Break this problem into two subproblems by setting 
(h + 1) equal to 10.440306509 and -10.440306509.

Subproblem 1
h + 1 = 10.440306509

Simplifying
h + 1 = 10.440306509

Reorder the terms:
1 + h = 10.440306509

Solving
1 + h = 10.440306509

Solving for variable 'h'.

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

Add '-1' to each side of the equation.
1 + -1 + h = 10.440306509 + -1

Combine like terms: 1 + -1 = 0
0 + h = 10.440306509 + -1
h = 10.440306509 + -1

Combine like terms: 10.440306509 + -1 = 9.440306509
h = 9.440306509

Simplifying
h = 9.440306509

Subproblem 2
h + 1 = -10.440306509

Simplifying
h + 1 = -10.440306509

Reorder the terms:
1 + h = -10.440306509

Solving
1 + h = -10.440306509

Solving for variable 'h'.

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

Add '-1' to each side of the equation.
1 + -1 + h = -10.440306509 + -1

Combine like terms: 1 + -1 = 0
0 + h = -10.440306509 + -1
h = -10.440306509 + -1

Combine like terms: -10.440306509 + -1 = -11.440306509
h = -11.440306509

Simplifying
h = -11.440306509

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {9.440306509, -11.440306509}