0=x^2+33x-90

Solution for 0=x^2+33x-90 equation:

Simplifying
0 = x2 + 33x + -90

Reorder the terms:
0 = -90 + 33x + x2

Solving
0 = -90 + 33x + x2

Solving for variable 'x'.

Combine like terms: 0 + 90 = 90
90 + -33x + -1x2 = -90 + 33x + x2 + 90 + -33x + -1x2

Reorder the terms:
90 + -33x + -1x2 = -90 + 90 + 33x + -33x + x2 + -1x2

Combine like terms: -90 + 90 = 0
90 + -33x + -1x2 = 0 + 33x + -33x + x2 + -1x2
90 + -33x + -1x2 = 33x + -33x + x2 + -1x2

Combine like terms: 33x + -33x = 0
90 + -33x + -1x2 = 0 + x2 + -1x2
90 + -33x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
90 + -33x + -1x2 = 0

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

Divide each side by '-1'.
-90 + 33x + x2 = 0

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 33x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 33x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 33x + x2 = 0 + 90
33x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
33x + x2 = 90

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 = 90 + 272.25

Reorder the terms:
272.25 + 33x + x2 = 90 + 272.25

Combine like terms: 90 + 272.25 = 362.25
272.25 + 33x + x2 = 362.25

Factor a perfect square on the left side:
(x + 16.5)(x + 16.5) = 362.25

Calculate the square root of the right side: 19.032866311

Break this problem into two subproblems by setting 
(x + 16.5) equal to 19.032866311 and -19.032866311.

Subproblem 1
x + 16.5 = 19.032866311

Simplifying
x + 16.5 = 19.032866311

Reorder the terms:
16.5 + x = 19.032866311

Solving
16.5 + x = 19.032866311

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 = 19.032866311 + -16.5

Combine like terms: 16.5 + -16.5 = 0.0
0.0 + x = 19.032866311 + -16.5
x = 19.032866311 + -16.5

Combine like terms: 19.032866311 + -16.5 = 2.532866311
x = 2.532866311

Simplifying
x = 2.532866311

Subproblem 2
x + 16.5 = -19.032866311

Simplifying
x + 16.5 = -19.032866311

Reorder the terms:
16.5 + x = -19.032866311

Solving
16.5 + x = -19.032866311

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 = -19.032866311 + -16.5

Combine like terms: 16.5 + -16.5 = 0.0
0.0 + x = -19.032866311 + -16.5
x = -19.032866311 + -16.5

Combine like terms: -19.032866311 + -16.5 = -35.532866311
x = -35.532866311

Simplifying
x = -35.532866311

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.532866311, -35.532866311}