h^2-12h-9=0

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Solution for h^2-12h-9=0 equation: 


Simplifying
h2 + -12h + -9 = 0

Reorder the terms:
-9 + -12h + h2 = 0

Solving
-9 + -12h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -12h + 9 + h2 = 0 + 9

Reorder the terms:
-9 + 9 + -12h + h2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -12h + h2 = 0 + 9
-12h + h2 = 0 + 9

Combine like terms: 0 + 9 = 9
-12h + h2 = 9

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 = 9 + 36

Reorder the terms:
36 + -12h + h2 = 9 + 36

Combine like terms: 9 + 36 = 45
36 + -12h + h2 = 45

Factor a perfect square on the left side:
(h + -6)(h + -6) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(h + -6) equal to 6.708203933 and -6.708203933.


Subproblem 1
h + -6 = 6.708203933

Simplifying
h + -6 = 6.708203933

Reorder the terms:
-6 + h = 6.708203933

Solving
-6 + h = 6.708203933

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 = 6.708203933 + 6

Combine like terms: -6 + 6 = 0
0 + h = 6.708203933 + 6
h = 6.708203933 + 6

Combine like terms: 6.708203933 + 6 = 12.708203933
h = 12.708203933

Simplifying
h = 12.708203933


Subproblem 2
h + -6 = -6.708203933

Simplifying
h + -6 = -6.708203933

Reorder the terms:
-6 + h = -6.708203933

Solving
-6 + h = -6.708203933

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 = -6.708203933 + 6

Combine like terms: -6 + 6 = 0
0 + h = -6.708203933 + 6
h = -6.708203933 + 6

Combine like terms: -6.708203933 + 6 = -0.708203933
h = -0.708203933

Simplifying
h = -0.708203933


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {12.708203933, -0.708203933}

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