Simplifying
x^{2} + -11.5x + -6 = 0
Reorder the terms:
-6 + -11.5x + x^{2} = 0
Solving
-6 + -11.5x + x^{2} = 0
Solving for variable 'x'.
Begin completing the square.
Move the constant term to the right:
Add '6' to each side of the equation.
-6 + -11.5x + 6 + x^{2} = 0 + 6
Reorder the terms:
-6 + 6 + -11.5x + x^{2} = 0 + 6
Combine like terms: -6 + 6 = 0
0 + -11.5x + x^{2} = 0 + 6
-11.5x + x^{2} = 0 + 6
Combine like terms: 0 + 6 = 6
-11.5x + x^{2} = 6
The x term is -11.5x. Take half its coefficient (-5.75).
Square it (33.0625) and add it to both sides.
Add '33.0625' to each side of the equation.
-11.5x + 33.0625 + x^{2} = 6 + 33.0625
Reorder the terms:
33.0625 + -11.5x + x^{2} = 6 + 33.0625
Combine like terms: 6 + 33.0625 = 39.0625
33.0625 + -11.5x + x^{2} = 39.0625
Factor a perfect square on the left side:
(x + -5.75)(x + -5.75) = 39.0625
Calculate the square root of the right side: 6.25
Break this problem into two subproblems by setting
(x + -5.75) equal to 6.25 and -6.25.
#### Subproblem 1

x + -5.75 = 6.25
Simplifying
x + -5.75 = 6.25
Reorder the terms:
-5.75 + x = 6.25
Solving
-5.75 + x = 6.25
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '5.75' to each side of the equation.
-5.75 + 5.75 + x = 6.25 + 5.75
Combine like terms: -5.75 + 5.75 = 0.00
0.00 + x = 6.25 + 5.75
x = 6.25 + 5.75
Combine like terms: 6.25 + 5.75 = 12
x = 12
Simplifying
x = 12
#### Subproblem 2

x + -5.75 = -6.25
Simplifying
x + -5.75 = -6.25
Reorder the terms:
-5.75 + x = -6.25
Solving
-5.75 + x = -6.25
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '5.75' to each side of the equation.
-5.75 + 5.75 + x = -6.25 + 5.75
Combine like terms: -5.75 + 5.75 = 0.00
0.00 + x = -6.25 + 5.75
x = -6.25 + 5.75
Combine like terms: -6.25 + 5.75 = -0.5
x = -0.5
Simplifying
x = -0.5
#### Solution

The solution to the problem is based on the solutions
from the subproblems.
x = {12, -0.5}