33=x^2-x

Solution for 33=x^2-x equation:

Simplifying
33 = x2 + -1x

Reorder the terms:
33 = -1x + x2

Solving
33 = -1x + x2

Solving for variable 'x'.

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

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

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

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

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

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + -1x + 33 + x2 = 0 + 33

Reorder the terms:
-33 + 33 + -1x + x2 = 0 + 33

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

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

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 33 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 33 + 0.25

Combine like terms: 33 + 0.25 = 33.25
0.25 + -1x + x2 = 33.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 33.25

Calculate the square root of the right side: 5.766281297

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5.766281297 and -5.766281297.

Subproblem 1
x + 0.5 = 5.766281297

Simplifying
x + 0.5 = 5.766281297

Reorder the terms:
0.5 + x = 5.766281297

Solving
0.5 + x = 5.766281297

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 5.766281297 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 5.766281297 + -0.5
x = 5.766281297 + -0.5

Combine like terms: 5.766281297 + -0.5 = 5.266281297
x = 5.266281297

Simplifying
x = 5.266281297

Subproblem 2
x + 0.5 = -5.766281297

Simplifying
x + 0.5 = -5.766281297

Reorder the terms:
0.5 + x = -5.766281297

Solving
0.5 + x = -5.766281297

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -5.766281297 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -5.766281297 + -0.5
x = -5.766281297 + -0.5

Combine like terms: -5.766281297 + -0.5 = -6.266281297
x = -6.266281297

Simplifying
x = -6.266281297

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.266281297, -6.266281297}