2h^2-14h-108=0

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Solution for 2h^2-14h-108=0 equation: 


Simplifying
2h2 + -14h + -108 = 0

Reorder the terms:
-108 + -14h + 2h2 = 0

Solving
-108 + -14h + 2h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-54 + -7h + h2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-54 + -7h + h2)' equal to zero and attempt to solve:

Simplifying
-54 + -7h + h2 = 0

Solving
-54 + -7h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + -7h + 54 + h2 = 0 + 54

Reorder the terms:
-54 + 54 + -7h + h2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + -7h + h2 = 0 + 54
-7h + h2 = 0 + 54

Combine like terms: 0 + 54 = 54
-7h + h2 = 54

The h term is -7h.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7h + 12.25 + h2 = 54 + 12.25

Reorder the terms:
12.25 + -7h + h2 = 54 + 12.25

Combine like terms: 54 + 12.25 = 66.25
12.25 + -7h + h2 = 66.25

Factor a perfect square on the left side:
(h + -3.5)(h + -3.5) = 66.25

Calculate the square root of the right side: 8.139410298

Break this problem into two subproblems by setting 
(h + -3.5) equal to 8.139410298 and -8.139410298.


Subproblem 1
h + -3.5 = 8.139410298

Simplifying
h + -3.5 = 8.139410298

Reorder the terms:
-3.5 + h = 8.139410298

Solving
-3.5 + h = 8.139410298

Solving for variable 'h'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + h = 8.139410298 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + h = 8.139410298 + 3.5
h = 8.139410298 + 3.5

Combine like terms: 8.139410298 + 3.5 = 11.639410298
h = 11.639410298

Simplifying
h = 11.639410298


Subproblem 2
h + -3.5 = -8.139410298

Simplifying
h + -3.5 = -8.139410298

Reorder the terms:
-3.5 + h = -8.139410298

Solving
-3.5 + h = -8.139410298

Solving for variable 'h'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + h = -8.139410298 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + h = -8.139410298 + 3.5
h = -8.139410298 + 3.5

Combine like terms: -8.139410298 + 3.5 = -4.639410298
h = -4.639410298

Simplifying
h = -4.639410298


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {11.639410298, -4.639410298}
Solution
h = {11.639410298, -4.639410298}

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