0=x^2-2x-33

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

Simplifying
0 = x2 + -2x + -33

Reorder the terms:
0 = -33 + -2x + x2

Solving
0 = -33 + -2x + x2

Solving for variable 'x'.

Combine like terms: 0 + 33 = 33
33 + 2x + -1x2 = -33 + -2x + x2 + 33 + 2x + -1x2

Reorder the terms:
33 + 2x + -1x2 = -33 + 33 + -2x + 2x + x2 + -1x2

Combine like terms: -33 + 33 = 0
33 + 2x + -1x2 = 0 + -2x + 2x + x2 + -1x2
33 + 2x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
33 + 2x + -1x2 = 0 + x2 + -1x2
33 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
33 + 2x + -1x2 = 0

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

Divide each side by '-1'.
-33 + -2x + x2 = 0

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + -2x + 33 + x2 = 0 + 33

Reorder the terms:
-33 + 33 + -2x + x2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + -2x + x2 = 0 + 33
-2x + x2 = 0 + 33

Combine like terms: 0 + 33 = 33
-2x + x2 = 33

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 33 + 1

Reorder the terms:
1 + -2x + x2 = 33 + 1

Combine like terms: 33 + 1 = 34
1 + -2x + x2 = 34

Factor a perfect square on the left side:
(x + -1)(x + -1) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(x + -1) equal to 5.830951895 and -5.830951895.

Subproblem 1
x + -1 = 5.830951895

Simplifying
x + -1 = 5.830951895

Reorder the terms:
-1 + x = 5.830951895

Solving
-1 + x = 5.830951895

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 5.830951895 + 1

Combine like terms: -1 + 1 = 0
0 + x = 5.830951895 + 1
x = 5.830951895 + 1

Combine like terms: 5.830951895 + 1 = 6.830951895
x = 6.830951895

Simplifying
x = 6.830951895

Subproblem 2
x + -1 = -5.830951895

Simplifying
x + -1 = -5.830951895

Reorder the terms:
-1 + x = -5.830951895

Solving
-1 + x = -5.830951895

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -5.830951895 + 1

Combine like terms: -1 + 1 = 0
0 + x = -5.830951895 + 1
x = -5.830951895 + 1

Combine like terms: -5.830951895 + 1 = -4.830951895
x = -4.830951895

Simplifying
x = -4.830951895

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.830951895, -4.830951895}