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Simplifying
x2 + -11.5x + -6 = 0

Reorder the terms:
-6 + -11.5x + x2 = 0

Solving
-6 + -11.5x + x2 = 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 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -11.5x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -11.5x + x2 = 0 + 6
-11.5x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-11.5x + x2 = 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 + x2 = 6 + 33.0625

Reorder the terms:
33.0625 + -11.5x + x2 = 6 + 33.0625

Combine like terms: 6 + 33.0625 = 39.0625
33.0625 + -11.5x + x2 = 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}
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