.5h+.3h(h-6)=16.6+2

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Solution for .5h+.3h(h-6)=16.6+2 equation: 


Simplifying
0.5h + 0.3h(h + -6) = 16.6 + 2

Reorder the terms:
0.5h + 0.3h(-6 + h) = 16.6 + 2
0.5h + (-6 * 0.3h + h * 0.3h) = 16.6 + 2
0.5h + (-1.8h + 0.3h2) = 16.6 + 2

Combine like terms: 0.5h + -1.8h = -1.3h
-1.3h + 0.3h2 = 16.6 + 2

Combine like terms: 16.6 + 2 = 18.6
-1.3h + 0.3h2 = 18.6

Solving
-1.3h + 0.3h2 = 18.6

Solving for variable 'h'.

Reorder the terms:
-18.6 + -1.3h + 0.3h2 = 18.6 + -18.6

Combine like terms: 18.6 + -18.6 = 0.0
-18.6 + -1.3h + 0.3h2 = 0.0

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

Divide each side by '0.3'.
-62 + -4.333333333h + h2 = 0

Move the constant term to the right:

Add '62' to each side of the equation.
-62 + -4.333333333h + 62 + h2 = 0 + 62

Reorder the terms:
-62 + 62 + -4.333333333h + h2 = 0 + 62

Combine like terms: -62 + 62 = 0
0 + -4.333333333h + h2 = 0 + 62
-4.333333333h + h2 = 0 + 62

Combine like terms: 0 + 62 = 62
-4.333333333h + h2 = 62

The h term is -4.333333333h.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333h + 4.694444446 + h2 = 62 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333h + h2 = 62 + 4.694444446

Combine like terms: 62 + 4.694444446 = 66.694444446
4.694444446 + -4.333333333h + h2 = 66.694444446

Factor a perfect square on the left side:
(h + -2.166666667)(h + -2.166666667) = 66.694444446

Calculate the square root of the right side: 8.166666667

Break this problem into two subproblems by setting 
(h + -2.166666667) equal to 8.166666667 and -8.166666667.


Subproblem 1
h + -2.166666667 = 8.166666667

Simplifying
h + -2.166666667 = 8.166666667

Reorder the terms:
-2.166666667 + h = 8.166666667

Solving
-2.166666667 + h = 8.166666667

Solving for variable 'h'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + h = 8.166666667 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + h = 8.166666667 + 2.166666667
h = 8.166666667 + 2.166666667

Combine like terms: 8.166666667 + 2.166666667 = 10.333333334
h = 10.333333334

Simplifying
h = 10.333333334


Subproblem 2
h + -2.166666667 = -8.166666667

Simplifying
h + -2.166666667 = -8.166666667

Reorder the terms:
-2.166666667 + h = -8.166666667

Solving
-2.166666667 + h = -8.166666667

Solving for variable 'h'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + h = -8.166666667 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + h = -8.166666667 + 2.166666667
h = -8.166666667 + 2.166666667

Combine like terms: -8.166666667 + 2.166666667 = -6
h = -6

Simplifying
h = -6


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {10.333333334, -6}

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