x^2-2x-32=0

Solution for x^2-2x-32=0 equation:

Simplifying
x2 + -2x + -32 = 0

Reorder the terms:
-32 + -2x + x2 = 0

Solving
-32 + -2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -2x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + -2x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -2x + x2 = 0 + 32
-2x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
-2x + x2 = 32

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 = 32 + 1

Reorder the terms:
1 + -2x + x2 = 32 + 1

Combine like terms: 32 + 1 = 33
1 + -2x + x2 = 33

Factor a perfect square on the left side:
(x + -1)(x + -1) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(x + -1) equal to 5.744562647 and -5.744562647.

Subproblem 1
x + -1 = 5.744562647

Simplifying
x + -1 = 5.744562647

Reorder the terms:
-1 + x = 5.744562647

Solving
-1 + x = 5.744562647

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 = 5.744562647 + 1

Combine like terms: -1 + 1 = 0
0 + x = 5.744562647 + 1
x = 5.744562647 + 1

Combine like terms: 5.744562647 + 1 = 6.744562647
x = 6.744562647

Simplifying
x = 6.744562647

Subproblem 2
x + -1 = -5.744562647

Simplifying
x + -1 = -5.744562647

Reorder the terms:
-1 + x = -5.744562647

Solving
-1 + x = -5.744562647

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 = -5.744562647 + 1

Combine like terms: -1 + 1 = 0
0 + x = -5.744562647 + 1
x = -5.744562647 + 1

Combine like terms: -5.744562647 + 1 = -4.744562647
x = -4.744562647

Simplifying
x = -4.744562647

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.744562647, -4.744562647}