3h^2+4h-1226=0

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Solution for 3h^2+4h-1226=0 equation: 


Simplifying
3h2 + 4h + -1226 = 0

Reorder the terms:
-1226 + 4h + 3h2 = 0

Solving
-1226 + 4h + 3h2 = 0

Solving for variable 'h'.

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

Divide each side by '3'.
-408.6666667 + 1.333333333h + h2 = 0

Move the constant term to the right:

Add '408.6666667' to each side of the equation.
-408.6666667 + 1.333333333h + 408.6666667 + h2 = 0 + 408.6666667

Reorder the terms:
-408.6666667 + 408.6666667 + 1.333333333h + h2 = 0 + 408.6666667

Combine like terms: -408.6666667 + 408.6666667 = 0.0000000
0.0000000 + 1.333333333h + h2 = 0 + 408.6666667
1.333333333h + h2 = 0 + 408.6666667

Combine like terms: 0 + 408.6666667 = 408.6666667
1.333333333h + h2 = 408.6666667

The h term is 1.333333333h.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333h + 0.4444444442 + h2 = 408.6666667 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333h + h2 = 408.6666667 + 0.4444444442

Combine like terms: 408.6666667 + 0.4444444442 = 409.1111111442
0.4444444442 + 1.333333333h + h2 = 409.1111111442

Factor a perfect square on the left side:
(h + 0.6666666665)(h + 0.6666666665) = 409.1111111442

Calculate the square root of the right side: 20.226495276

Break this problem into two subproblems by setting 
(h + 0.6666666665) equal to 20.226495276 and -20.226495276.


Subproblem 1
h + 0.6666666665 = 20.226495276

Simplifying
h + 0.6666666665 = 20.226495276

Reorder the terms:
0.6666666665 + h = 20.226495276

Solving
0.6666666665 + h = 20.226495276

Solving for variable 'h'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + h = 20.226495276 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + h = 20.226495276 + -0.6666666665
h = 20.226495276 + -0.6666666665

Combine like terms: 20.226495276 + -0.6666666665 = 19.5598286095
h = 19.5598286095

Simplifying
h = 19.5598286095


Subproblem 2
h + 0.6666666665 = -20.226495276

Simplifying
h + 0.6666666665 = -20.226495276

Reorder the terms:
0.6666666665 + h = -20.226495276

Solving
0.6666666665 + h = -20.226495276

Solving for variable 'h'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + h = -20.226495276 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + h = -20.226495276 + -0.6666666665
h = -20.226495276 + -0.6666666665

Combine like terms: -20.226495276 + -0.6666666665 = -20.8931619425
h = -20.8931619425

Simplifying
h = -20.8931619425


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {19.5598286095, -20.8931619425}

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