8h^2-8h-2=0

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

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

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

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

Solving for variable 'h'.

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -4h + 4h2)' equal to zero and attempt to solve:

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

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

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

Divide each side by '4'.
-0.25 + -1h + h2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -1h + 0.25 + h2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -1h + h2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -1h + h2 = 0 + 0.25
-1h + h2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-1h + h2 = 0.25

The h term is -1h.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1h + 0.25 + h2 = 0.25 + 0.25

Reorder the terms:
0.25 + -1h + h2 = 0.25 + 0.25

Combine like terms: 0.25 + 0.25 = 0.5
0.25 + -1h + h2 = 0.5

Factor a perfect square on the left side:
(h + -0.5)(h + -0.5) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(h + -0.5) equal to 0.707106781 and -0.707106781.

Subproblem 1
h + -0.5 = 0.707106781

Simplifying
h + -0.5 = 0.707106781

Reorder the terms:
-0.5 + h = 0.707106781

Solving
-0.5 + h = 0.707106781

Solving for variable 'h'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + h = 0.707106781 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + h = 0.707106781 + 0.5
h = 0.707106781 + 0.5

Combine like terms: 0.707106781 + 0.5 = 1.207106781
h = 1.207106781

Simplifying
h = 1.207106781

Subproblem 2
h + -0.5 = -0.707106781

Simplifying
h + -0.5 = -0.707106781

Reorder the terms:
-0.5 + h = -0.707106781

Solving
-0.5 + h = -0.707106781

Solving for variable 'h'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + h = -0.707106781 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + h = -0.707106781 + 0.5
h = -0.707106781 + 0.5

Combine like terms: -0.707106781 + 0.5 = -0.207106781
h = -0.207106781

Simplifying
h = -0.207106781

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {1.207106781, -0.207106781}
Solution
h = {1.207106781, -0.207106781}