60h^2+280h+44=

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Solution for 60h^2+280h+44= equation:


Simplifying
60h2 + 280h + 44 = 0

Reorder the terms:
44 + 280h + 60h2 = 0

Solving
44 + 280h + 60h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '4'.
4(11 + 70h + 15h2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(11 + 70h + 15h2)' equal to zero and attempt to solve:

Simplifying
11 + 70h + 15h2 = 0

Solving
11 + 70h + 15h2 = 0

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

Divide each side by '15'.
0.7333333333 + 4.666666667h + h2 = 0

Move the constant term to the right:

Add '-0.7333333333' to each side of the equation.
0.7333333333 + 4.666666667h + -0.7333333333 + h2 = 0 + -0.7333333333

Reorder the terms:
0.7333333333 + -0.7333333333 + 4.666666667h + h2 = 0 + -0.7333333333

Combine like terms: 0.7333333333 + -0.7333333333 = 0.0000000000
0.0000000000 + 4.666666667h + h2 = 0 + -0.7333333333
4.666666667h + h2 = 0 + -0.7333333333

Combine like terms: 0 + -0.7333333333 = -0.7333333333
4.666666667h + h2 = -0.7333333333

The h term is 4.666666667h.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667h + 5.444444448 + h2 = -0.7333333333 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667h + h2 = -0.7333333333 + 5.444444448

Combine like terms: -0.7333333333 + 5.444444448 = 4.7111111147
5.444444448 + 4.666666667h + h2 = 4.7111111147

Factor a perfect square on the left side:
(h + 2.333333334)(h + 2.333333334) = 4.7111111147

Calculate the square root of the right side: 2.170509414

Break this problem into two subproblems by setting 
(h + 2.333333334) equal to 2.170509414 and -2.170509414.


Subproblem 1
h + 2.333333334 = 2.170509414

Simplifying
h + 2.333333334 = 2.170509414

Reorder the terms:
2.333333334 + h = 2.170509414

Solving
2.333333334 + h = 2.170509414

Solving for variable 'h'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + h = 2.170509414 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + h = 2.170509414 + -2.333333334
h = 2.170509414 + -2.333333334

Combine like terms: 2.170509414 + -2.333333334 = -0.16282392
h = -0.16282392

Simplifying
h = -0.16282392


Subproblem 2
h + 2.333333334 = -2.170509414

Simplifying
h + 2.333333334 = -2.170509414

Reorder the terms:
2.333333334 + h = -2.170509414

Solving
2.333333334 + h = -2.170509414

Solving for variable 'h'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + h = -2.170509414 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + h = -2.170509414 + -2.333333334
h = -2.170509414 + -2.333333334

Combine like terms: -2.170509414 + -2.333333334 = -4.503842748
h = -4.503842748

Simplifying
h = -4.503842748


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {-0.16282392, -4.503842748}
Solution
h = {-0.16282392, -4.503842748}

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