12x^2-116x+204=0

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Solution for 12x^2-116x+204=0 equation: 


Simplifying
12x2 + -116x + 204 = 0

Reorder the terms:
204 + -116x + 12x2 = 0

Solving
204 + -116x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(51 + -29x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(51 + -29x + 3x2)' equal to zero and attempt to solve:

Simplifying
51 + -29x + 3x2 = 0

Solving
51 + -29x + 3x2 = 0

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

Divide each side by '3'.
17 + -9.666666667x + x2 = 0

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + -9.666666667x + -17 + x2 = 0 + -17

Reorder the terms:
17 + -17 + -9.666666667x + x2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -9.666666667x + x2 = 0 + -17
-9.666666667x + x2 = 0 + -17

Combine like terms: 0 + -17 = -17
-9.666666667x + x2 = -17

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 = -17 + 23.36111112

Reorder the terms:
23.36111112 + -9.666666667x + x2 = -17 + 23.36111112

Combine like terms: -17 + 23.36111112 = 6.36111112
23.36111112 + -9.666666667x + x2 = 6.36111112

Factor a perfect square on the left side:
(x + -4.833333334)(x + -4.833333334) = 6.36111112

Calculate the square root of the right side: 2.522124327

Break this problem into two subproblems by setting 
(x + -4.833333334) equal to 2.522124327 and -2.522124327.


Subproblem 1
x + -4.833333334 = 2.522124327

Simplifying
x + -4.833333334 = 2.522124327

Reorder the terms:
-4.833333334 + x = 2.522124327

Solving
-4.833333334 + x = 2.522124327

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 = 2.522124327 + 4.833333334

Combine like terms: -4.833333334 + 4.833333334 = 0.000000000
0.000000000 + x = 2.522124327 + 4.833333334
x = 2.522124327 + 4.833333334

Combine like terms: 2.522124327 + 4.833333334 = 7.355457661
x = 7.355457661

Simplifying
x = 7.355457661


Subproblem 2
x + -4.833333334 = -2.522124327

Simplifying
x + -4.833333334 = -2.522124327

Reorder the terms:
-4.833333334 + x = -2.522124327

Solving
-4.833333334 + x = -2.522124327

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 = -2.522124327 + 4.833333334

Combine like terms: -4.833333334 + 4.833333334 = 0.000000000
0.000000000 + x = -2.522124327 + 4.833333334
x = -2.522124327 + 4.833333334

Combine like terms: -2.522124327 + 4.833333334 = 2.311209007
x = 2.311209007

Simplifying
x = 2.311209007


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.355457661, 2.311209007}
Solution
x = {7.355457661, 2.311209007}

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