12x^2-116x-198=0

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Solution for 12x^2-116x-198=0 equation: 


Simplifying
12x2 + -116x + -198 = 0

Reorder the terms:
-198 + -116x + 12x2 = 0

Solving
-198 + -116x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-99 + -58x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-99 + -58x + 6x2)' equal to zero and attempt to solve:

Simplifying
-99 + -58x + 6x2 = 0

Solving
-99 + -58x + 6x2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
-16.5 + -9.666666667x + x2 = 0

Move the constant term to the right:

Add '16.5' to each side of the equation.
-16.5 + -9.666666667x + 16.5 + x2 = 0 + 16.5

Reorder the terms:
-16.5 + 16.5 + -9.666666667x + x2 = 0 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + -9.666666667x + x2 = 0 + 16.5
-9.666666667x + x2 = 0 + 16.5

Combine like terms: 0 + 16.5 = 16.5
-9.666666667x + x2 = 16.5

The x term is -9.666666667x.  Take half its coefficient (-4.833333334).
Square it (23.36111112) and add it to both sides.

Add '23.36111112' to each side of the equation.
-9.666666667x + 23.36111112 + x2 = 16.5 + 23.36111112

Reorder the terms:
23.36111112 + -9.666666667x + x2 = 16.5 + 23.36111112

Combine like terms: 16.5 + 23.36111112 = 39.86111112
23.36111112 + -9.666666667x + x2 = 39.86111112

Factor a perfect square on the left side:
(x + -4.833333334)(x + -4.833333334) = 39.86111112

Calculate the square root of the right side: 6.313565642

Break this problem into two subproblems by setting 
(x + -4.833333334) equal to 6.313565642 and -6.313565642.


Subproblem 1
x + -4.833333334 = 6.313565642

Simplifying
x + -4.833333334 = 6.313565642

Reorder the terms:
-4.833333334 + x = 6.313565642

Solving
-4.833333334 + x = 6.313565642

Solving for variable 'x'.

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

Add '4.833333334' to each side of the equation.
-4.833333334 + 4.833333334 + x = 6.313565642 + 4.833333334

Combine like terms: -4.833333334 + 4.833333334 = 0.000000000
0.000000000 + x = 6.313565642 + 4.833333334
x = 6.313565642 + 4.833333334

Combine like terms: 6.313565642 + 4.833333334 = 11.146898976
x = 11.146898976

Simplifying
x = 11.146898976


Subproblem 2
x + -4.833333334 = -6.313565642

Simplifying
x + -4.833333334 = -6.313565642

Reorder the terms:
-4.833333334 + x = -6.313565642

Solving
-4.833333334 + x = -6.313565642

Solving for variable 'x'.

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

Add '4.833333334' to each side of the equation.
-4.833333334 + 4.833333334 + x = -6.313565642 + 4.833333334

Combine like terms: -4.833333334 + 4.833333334 = 0.000000000
0.000000000 + x = -6.313565642 + 4.833333334
x = -6.313565642 + 4.833333334

Combine like terms: -6.313565642 + 4.833333334 = -1.480232308
x = -1.480232308

Simplifying
x = -1.480232308


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.146898976, -1.480232308}
Solution
x = {11.146898976, -1.480232308}

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