h^2+12h-14=0

Solution for h^2+12h-14=0 equation:

Simplifying
h2 + 12h + -14 = 0

Reorder the terms:
-14 + 12h + h2 = 0

Solving
-14 + 12h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 12h + 14 + h2 = 0 + 14

Reorder the terms:
-14 + 14 + 12h + h2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 12h + h2 = 0 + 14
12h + h2 = 0 + 14

Combine like terms: 0 + 14 = 14
12h + h2 = 14

The h term is 12h.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12h + 36 + h2 = 14 + 36

Reorder the terms:
36 + 12h + h2 = 14 + 36

Combine like terms: 14 + 36 = 50
36 + 12h + h2 = 50

Factor a perfect square on the left side:
(h + 6)(h + 6) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(h + 6) equal to 7.071067812 and -7.071067812.

Subproblem 1
h + 6 = 7.071067812

Simplifying
h + 6 = 7.071067812

Reorder the terms:
6 + h = 7.071067812

Solving
6 + h = 7.071067812

Solving for variable 'h'.

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

Add '-6' to each side of the equation.
6 + -6 + h = 7.071067812 + -6

Combine like terms: 6 + -6 = 0
0 + h = 7.071067812 + -6
h = 7.071067812 + -6

Combine like terms: 7.071067812 + -6 = 1.071067812
h = 1.071067812

Simplifying
h = 1.071067812

Subproblem 2
h + 6 = -7.071067812

Simplifying
h + 6 = -7.071067812

Reorder the terms:
6 + h = -7.071067812

Solving
6 + h = -7.071067812

Solving for variable 'h'.

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

Add '-6' to each side of the equation.
6 + -6 + h = -7.071067812 + -6

Combine like terms: 6 + -6 = 0
0 + h = -7.071067812 + -6
h = -7.071067812 + -6

Combine like terms: -7.071067812 + -6 = -13.071067812
h = -13.071067812

Simplifying
h = -13.071067812

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {1.071067812, -13.071067812}