2x^2-12x-66=0

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Solution for 2x^2-12x-66=0 equation: 


Simplifying
2x2 + -12x + -66 = 0

Reorder the terms:
-66 + -12x + 2x2 = 0

Solving
-66 + -12x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-33 + -6x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-33 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-33 + -6x + x2 = 0

Solving
-33 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + -6x + 33 + x2 = 0 + 33

Reorder the terms:
-33 + 33 + -6x + x2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + -6x + x2 = 0 + 33
-6x + x2 = 0 + 33

Combine like terms: 0 + 33 = 33
-6x + x2 = 33

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 33 + 9

Reorder the terms:
9 + -6x + x2 = 33 + 9

Combine like terms: 33 + 9 = 42
9 + -6x + x2 = 42

Factor a perfect square on the left side:
(x + -3)(x + -3) = 42

Calculate the square root of the right side: 6.480740698

Break this problem into two subproblems by setting 
(x + -3) equal to 6.480740698 and -6.480740698.


Subproblem 1
x + -3 = 6.480740698

Simplifying
x + -3 = 6.480740698

Reorder the terms:
-3 + x = 6.480740698

Solving
-3 + x = 6.480740698

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 6.480740698 + 3

Combine like terms: -3 + 3 = 0
0 + x = 6.480740698 + 3
x = 6.480740698 + 3

Combine like terms: 6.480740698 + 3 = 9.480740698
x = 9.480740698

Simplifying
x = 9.480740698


Subproblem 2
x + -3 = -6.480740698

Simplifying
x + -3 = -6.480740698

Reorder the terms:
-3 + x = -6.480740698

Solving
-3 + x = -6.480740698

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -6.480740698 + 3

Combine like terms: -3 + 3 = 0
0 + x = -6.480740698 + 3
x = -6.480740698 + 3

Combine like terms: -6.480740698 + 3 = -3.480740698
x = -3.480740698

Simplifying
x = -3.480740698


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.480740698, -3.480740698}
Solution
x = {9.480740698, -3.480740698}

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