8h^2-2h-2=0

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Solution for 8h^2-2h-2=0 equation: 


Simplifying
8h2 + -2h + -2 = 0

Reorder the terms:
-2 + -2h + 8h2 = 0

Solving
-2 + -2h + 8h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -1h + 4h2) = 0

Ignore the factor 2.

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

Simplifying
-1 + -1h + 4h2 = 0

Solving
-1 + -1h + 4h2 = 0

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

Divide each side by '4'.
-0.25 + -0.25h + h2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -0.25h + 0.25 + h2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -0.25h + h2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -0.25h + h2 = 0 + 0.25
-0.25h + h2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-0.25h + h2 = 0.25

The h term is -0.25h.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25h + 0.015625 + h2 = 0.25 + 0.015625

Reorder the terms:
0.015625 + -0.25h + h2 = 0.25 + 0.015625

Combine like terms: 0.25 + 0.015625 = 0.265625
0.015625 + -0.25h + h2 = 0.265625

Factor a perfect square on the left side:
(h + -0.125)(h + -0.125) = 0.265625

Calculate the square root of the right side: 0.515388203

Break this problem into two subproblems by setting 
(h + -0.125) equal to 0.515388203 and -0.515388203.


Subproblem 1
h + -0.125 = 0.515388203

Simplifying
h + -0.125 = 0.515388203

Reorder the terms:
-0.125 + h = 0.515388203

Solving
-0.125 + h = 0.515388203

Solving for variable 'h'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + h = 0.515388203 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + h = 0.515388203 + 0.125
h = 0.515388203 + 0.125

Combine like terms: 0.515388203 + 0.125 = 0.640388203
h = 0.640388203

Simplifying
h = 0.640388203


Subproblem 2
h + -0.125 = -0.515388203

Simplifying
h + -0.125 = -0.515388203

Reorder the terms:
-0.125 + h = -0.515388203

Solving
-0.125 + h = -0.515388203

Solving for variable 'h'.

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

Add '0.125' to each side of the equation.
-0.125 + 0.125 + h = -0.515388203 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + h = -0.515388203 + 0.125
h = -0.515388203 + 0.125

Combine like terms: -0.515388203 + 0.125 = -0.390388203
h = -0.390388203

Simplifying
h = -0.390388203


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {0.640388203, -0.390388203}
Solution
h = {0.640388203, -0.390388203}

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