h^2+2h-58=0

Solution for h^2+2h-58=0 equation:

Simplifying
h2 + 2h + -58 = 0

Reorder the terms:
-58 + 2h + h2 = 0

Solving
-58 + 2h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '58' to each side of the equation.
-58 + 2h + 58 + h2 = 0 + 58

Reorder the terms:
-58 + 58 + 2h + h2 = 0 + 58

Combine like terms: -58 + 58 = 0
0 + 2h + h2 = 0 + 58
2h + h2 = 0 + 58

Combine like terms: 0 + 58 = 58
2h + h2 = 58

The h term is 2h.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2h + 1 + h2 = 58 + 1

Reorder the terms:
1 + 2h + h2 = 58 + 1

Combine like terms: 58 + 1 = 59
1 + 2h + h2 = 59

Factor a perfect square on the left side:
(h + 1)(h + 1) = 59

Calculate the square root of the right side: 7.681145748

Break this problem into two subproblems by setting 
(h + 1) equal to 7.681145748 and -7.681145748.

Subproblem 1
h + 1 = 7.681145748

Simplifying
h + 1 = 7.681145748

Reorder the terms:
1 + h = 7.681145748

Solving
1 + h = 7.681145748

Solving for variable 'h'.

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

Add '-1' to each side of the equation.
1 + -1 + h = 7.681145748 + -1

Combine like terms: 1 + -1 = 0
0 + h = 7.681145748 + -1
h = 7.681145748 + -1

Combine like terms: 7.681145748 + -1 = 6.681145748
h = 6.681145748

Simplifying
h = 6.681145748

Subproblem 2
h + 1 = -7.681145748

Simplifying
h + 1 = -7.681145748

Reorder the terms:
1 + h = -7.681145748

Solving
1 + h = -7.681145748

Solving for variable 'h'.

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

Add '-1' to each side of the equation.
1 + -1 + h = -7.681145748 + -1

Combine like terms: 1 + -1 = 0
0 + h = -7.681145748 + -1
h = -7.681145748 + -1

Combine like terms: -7.681145748 + -1 = -8.681145748
h = -8.681145748

Simplifying
h = -8.681145748

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {6.681145748, -8.681145748}