-33+h^2+4h=0

Solution for -33+h^2+4h=0 equation:

Simplifying
-33 + h2 + 4h = 0

Reorder the terms:
-33 + 4h + h2 = 0

Solving
-33 + 4h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + 4h + 33 + h2 = 0 + 33

Reorder the terms:
-33 + 33 + 4h + h2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + 4h + h2 = 0 + 33
4h + h2 = 0 + 33

Combine like terms: 0 + 33 = 33
4h + h2 = 33

The h term is 4h.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4h + 4 + h2 = 33 + 4

Reorder the terms:
4 + 4h + h2 = 33 + 4

Combine like terms: 33 + 4 = 37
4 + 4h + h2 = 37

Factor a perfect square on the left side:
(h + 2)(h + 2) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(h + 2) equal to 6.08276253 and -6.08276253.

Subproblem 1
h + 2 = 6.08276253

Simplifying
h + 2 = 6.08276253

Reorder the terms:
2 + h = 6.08276253

Solving
2 + h = 6.08276253

Solving for variable 'h'.

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

Add '-2' to each side of the equation.
2 + -2 + h = 6.08276253 + -2

Combine like terms: 2 + -2 = 0
0 + h = 6.08276253 + -2
h = 6.08276253 + -2

Combine like terms: 6.08276253 + -2 = 4.08276253
h = 4.08276253

Simplifying
h = 4.08276253

Subproblem 2
h + 2 = -6.08276253

Simplifying
h + 2 = -6.08276253

Reorder the terms:
2 + h = -6.08276253

Solving
2 + h = -6.08276253

Solving for variable 'h'.

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

Add '-2' to each side of the equation.
2 + -2 + h = -6.08276253 + -2

Combine like terms: 2 + -2 = 0
0 + h = -6.08276253 + -2
h = -6.08276253 + -2

Combine like terms: -6.08276253 + -2 = -8.08276253
h = -8.08276253

Simplifying
h = -8.08276253

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {4.08276253, -8.08276253}