10h^2-2h-5=0

Solution for 10h^2-2h-5=0 equation:

Simplifying
10h2 + -2h + -5 = 0

Reorder the terms:
-5 + -2h + 10h2 = 0

Solving
-5 + -2h + 10h2 = 0

Solving for variable 'h'.

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

Divide each side by '10'.
-0.5 + -0.2h + h2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.2h + 0.5 + h2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.2h + h2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.2h + h2 = 0 + 0.5
-0.2h + h2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.2h + h2 = 0.5

The h term is -0.2h.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2h + 0.01 + h2 = 0.5 + 0.01

Reorder the terms:
0.01 + -0.2h + h2 = 0.5 + 0.01

Combine like terms: 0.5 + 0.01 = 0.51
0.01 + -0.2h + h2 = 0.51

Factor a perfect square on the left side:
(h + -0.1)(h + -0.1) = 0.51

Calculate the square root of the right side: 0.714142843

Break this problem into two subproblems by setting 
(h + -0.1) equal to 0.714142843 and -0.714142843.

Subproblem 1
h + -0.1 = 0.714142843

Simplifying
h + -0.1 = 0.714142843

Reorder the terms:
-0.1 + h = 0.714142843

Solving
-0.1 + h = 0.714142843

Solving for variable 'h'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + h = 0.714142843 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + h = 0.714142843 + 0.1
h = 0.714142843 + 0.1

Combine like terms: 0.714142843 + 0.1 = 0.814142843
h = 0.814142843

Simplifying
h = 0.814142843

Subproblem 2
h + -0.1 = -0.714142843

Simplifying
h + -0.1 = -0.714142843

Reorder the terms:
-0.1 + h = -0.714142843

Solving
-0.1 + h = -0.714142843

Solving for variable 'h'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + h = -0.714142843 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + h = -0.714142843 + 0.1
h = -0.714142843 + 0.1

Combine like terms: -0.714142843 + 0.1 = -0.614142843
h = -0.614142843

Simplifying
h = -0.614142843

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {0.814142843, -0.614142843}