x^2+33x+37=0

Solution for x^2+33x+37=0 equation:

Simplifying
x2 + 33x + 37 = 0

Reorder the terms:
37 + 33x + x2 = 0

Solving
37 + 33x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-37' to each side of the equation.
37 + 33x + -37 + x2 = 0 + -37

Reorder the terms:
37 + -37 + 33x + x2 = 0 + -37

Combine like terms: 37 + -37 = 0
0 + 33x + x2 = 0 + -37
33x + x2 = 0 + -37

Combine like terms: 0 + -37 = -37
33x + x2 = -37

The x term is 33x.  Take half its coefficient (16.5).
Square it (272.25) and add it to both sides.

Add '272.25' to each side of the equation.
33x + 272.25 + x2 = -37 + 272.25

Reorder the terms:
272.25 + 33x + x2 = -37 + 272.25

Combine like terms: -37 + 272.25 = 235.25
272.25 + 33x + x2 = 235.25

Factor a perfect square on the left side:
(x + 16.5)(x + 16.5) = 235.25

Calculate the square root of the right side: 15.33786165

Break this problem into two subproblems by setting 
(x + 16.5) equal to 15.33786165 and -15.33786165.

Subproblem 1
x + 16.5 = 15.33786165

Simplifying
x + 16.5 = 15.33786165

Reorder the terms:
16.5 + x = 15.33786165

Solving
16.5 + x = 15.33786165

Solving for variable 'x'.

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

Add '-16.5' to each side of the equation.
16.5 + -16.5 + x = 15.33786165 + -16.5

Combine like terms: 16.5 + -16.5 = 0.0
0.0 + x = 15.33786165 + -16.5
x = 15.33786165 + -16.5

Combine like terms: 15.33786165 + -16.5 = -1.16213835
x = -1.16213835

Simplifying
x = -1.16213835

Subproblem 2
x + 16.5 = -15.33786165

Simplifying
x + 16.5 = -15.33786165

Reorder the terms:
16.5 + x = -15.33786165

Solving
16.5 + x = -15.33786165

Solving for variable 'x'.

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

Add '-16.5' to each side of the equation.
16.5 + -16.5 + x = -15.33786165 + -16.5

Combine like terms: 16.5 + -16.5 = 0.0
0.0 + x = -15.33786165 + -16.5
x = -15.33786165 + -16.5

Combine like terms: -15.33786165 + -16.5 = -31.83786165
x = -31.83786165

Simplifying
x = -31.83786165

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.16213835, -31.83786165}