x^2-11x-32=0

Solution for x^2-11x-32=0 equation:

Simplifying
x2 + -11x + -32 = 0

Reorder the terms:
-32 + -11x + x2 = 0

Solving
-32 + -11x + 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 + -11x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + -11x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -11x + x2 = 0 + 32
-11x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
-11x + x2 = 32

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = 32 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 32 + 30.25

Combine like terms: 32 + 30.25 = 62.25
30.25 + -11x + x2 = 62.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 62.25

Calculate the square root of the right side: 7.889866919

Break this problem into two subproblems by setting 
(x + -5.5) equal to 7.889866919 and -7.889866919.

Subproblem 1
x + -5.5 = 7.889866919

Simplifying
x + -5.5 = 7.889866919

Reorder the terms:
-5.5 + x = 7.889866919

Solving
-5.5 + x = 7.889866919

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 7.889866919 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 7.889866919 + 5.5
x = 7.889866919 + 5.5

Combine like terms: 7.889866919 + 5.5 = 13.389866919
x = 13.389866919

Simplifying
x = 13.389866919

Subproblem 2
x + -5.5 = -7.889866919

Simplifying
x + -5.5 = -7.889866919

Reorder the terms:
-5.5 + x = -7.889866919

Solving
-5.5 + x = -7.889866919

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -7.889866919 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -7.889866919 + 5.5
x = -7.889866919 + 5.5

Combine like terms: -7.889866919 + 5.5 = -2.389866919
x = -2.389866919

Simplifying
x = -2.389866919

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.389866919, -2.389866919}