16h^2-12h-36=0

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Solution for 16h^2-12h-36=0 equation: 


Simplifying
16h2 + -12h + -36 = 0

Reorder the terms:
-36 + -12h + 16h2 = 0

Solving
-36 + -12h + 16h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + -3h + 4h2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-9 + -3h + 4h2)' equal to zero and attempt to solve:

Simplifying
-9 + -3h + 4h2 = 0

Solving
-9 + -3h + 4h2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-2.25 + -0.75h + h2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -0.75h + 2.25 + h2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -0.75h + h2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -0.75h + h2 = 0 + 2.25
-0.75h + h2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-0.75h + h2 = 2.25

The h term is -0.75h.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75h + 0.140625 + h2 = 2.25 + 0.140625

Reorder the terms:
0.140625 + -0.75h + h2 = 2.25 + 0.140625

Combine like terms: 2.25 + 0.140625 = 2.390625
0.140625 + -0.75h + h2 = 2.390625

Factor a perfect square on the left side:
(h + -0.375)(h + -0.375) = 2.390625

Calculate the square root of the right side: 1.54616461

Break this problem into two subproblems by setting 
(h + -0.375) equal to 1.54616461 and -1.54616461.


Subproblem 1
h + -0.375 = 1.54616461

Simplifying
h + -0.375 = 1.54616461

Reorder the terms:
-0.375 + h = 1.54616461

Solving
-0.375 + h = 1.54616461

Solving for variable 'h'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + h = 1.54616461 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + h = 1.54616461 + 0.375
h = 1.54616461 + 0.375

Combine like terms: 1.54616461 + 0.375 = 1.92116461
h = 1.92116461

Simplifying
h = 1.92116461


Subproblem 2
h + -0.375 = -1.54616461

Simplifying
h + -0.375 = -1.54616461

Reorder the terms:
-0.375 + h = -1.54616461

Solving
-0.375 + h = -1.54616461

Solving for variable 'h'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + h = -1.54616461 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + h = -1.54616461 + 0.375
h = -1.54616461 + 0.375

Combine like terms: -1.54616461 + 0.375 = -1.17116461
h = -1.17116461

Simplifying
h = -1.17116461


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {1.92116461, -1.17116461}
Solution
h = {1.92116461, -1.17116461}

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