100=h^2+5*h

Solution for 100=h^2+5*h equation:

Simplifying
100 = h2 + 5h

Reorder the terms:
100 = 5h + h2

Solving
100 = 5h + h2

Solving for variable 'h'.

Reorder the terms:
100 + -5h + -1h2 = 5h + -5h + h2 + -1h2

Combine like terms: 5h + -5h = 0
100 + -5h + -1h2 = 0 + h2 + -1h2
100 + -5h + -1h2 = h2 + -1h2

Combine like terms: h2 + -1h2 = 0
100 + -5h + -1h2 = 0

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

Divide each side by '-1'.
-100 + 5h + h2 = 0

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 5h + 100 + h2 = 0 + 100

Reorder the terms:
-100 + 100 + 5h + h2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 5h + h2 = 0 + 100
5h + h2 = 0 + 100

Combine like terms: 0 + 100 = 100
5h + h2 = 100

The h term is 5h.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5h + 6.25 + h2 = 100 + 6.25

Reorder the terms:
6.25 + 5h + h2 = 100 + 6.25

Combine like terms: 100 + 6.25 = 106.25
6.25 + 5h + h2 = 106.25

Factor a perfect square on the left side:
(h + 2.5)(h + 2.5) = 106.25

Calculate the square root of the right side: 10.307764064

Break this problem into two subproblems by setting 
(h + 2.5) equal to 10.307764064 and -10.307764064.

Subproblem 1
h + 2.5 = 10.307764064

Simplifying
h + 2.5 = 10.307764064

Reorder the terms:
2.5 + h = 10.307764064

Solving
2.5 + h = 10.307764064

Solving for variable 'h'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + h = 10.307764064 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + h = 10.307764064 + -2.5
h = 10.307764064 + -2.5

Combine like terms: 10.307764064 + -2.5 = 7.807764064
h = 7.807764064

Simplifying
h = 7.807764064

Subproblem 2
h + 2.5 = -10.307764064

Simplifying
h + 2.5 = -10.307764064

Reorder the terms:
2.5 + h = -10.307764064

Solving
2.5 + h = -10.307764064

Solving for variable 'h'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + h = -10.307764064 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + h = -10.307764064 + -2.5
h = -10.307764064 + -2.5

Combine like terms: -10.307764064 + -2.5 = -12.807764064
h = -12.807764064

Simplifying
h = -12.807764064

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {7.807764064, -12.807764064}