(2*6.5-h)*h=0.64

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Solution for (2*6.5-h)*h=0.64 equation: 


Simplifying
(2 * 6.5 + -1h) * h = 0.64

Multiply 2 * 6.5
(13 + -1h) * h = 0.64

Reorder the terms for easier multiplication:
h(13 + -1h) = 0.64
(13 * h + -1h * h) = 0.64
(13h + -1h2) = 0.64

Solving
13h + -1h2 = 0.64

Solving for variable 'h'.

Reorder the terms:
-0.64 + 13h + -1h2 = 0.64 + -0.64

Combine like terms: 0.64 + -0.64 = 0.00
-0.64 + 13h + -1h2 = 0.00

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
0.64 + -13h + h2 = 0.00

Move the constant term to the right:

Add '-0.64' to each side of the equation.
0.64 + -13h + -0.64 + h2 = 0.00 + -0.64

Reorder the terms:
0.64 + -0.64 + -13h + h2 = 0.00 + -0.64

Combine like terms: 0.64 + -0.64 = 0.00
0.00 + -13h + h2 = 0.00 + -0.64
-13h + h2 = 0.00 + -0.64

Combine like terms: 0.00 + -0.64 = -0.64
-13h + h2 = -0.64

The h term is -13h.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13h + 42.25 + h2 = -0.64 + 42.25

Reorder the terms:
42.25 + -13h + h2 = -0.64 + 42.25

Combine like terms: -0.64 + 42.25 = 41.61
42.25 + -13h + h2 = 41.61

Factor a perfect square on the left side:
(h + -6.5)(h + -6.5) = 41.61

Calculate the square root of the right side: 6.450581369

Break this problem into two subproblems by setting 
(h + -6.5) equal to 6.450581369 and -6.450581369.


Subproblem 1
h + -6.5 = 6.450581369

Simplifying
h + -6.5 = 6.450581369

Reorder the terms:
-6.5 + h = 6.450581369

Solving
-6.5 + h = 6.450581369

Solving for variable 'h'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + h = 6.450581369 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + h = 6.450581369 + 6.5
h = 6.450581369 + 6.5

Combine like terms: 6.450581369 + 6.5 = 12.950581369
h = 12.950581369

Simplifying
h = 12.950581369


Subproblem 2
h + -6.5 = -6.450581369

Simplifying
h + -6.5 = -6.450581369

Reorder the terms:
-6.5 + h = -6.450581369

Solving
-6.5 + h = -6.450581369

Solving for variable 'h'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + h = -6.450581369 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + h = -6.450581369 + 6.5
h = -6.450581369 + 6.5

Combine like terms: -6.450581369 + 6.5 = 0.049418631
h = 0.049418631

Simplifying
h = 0.049418631


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {12.950581369, 0.049418631}

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