12x^2-66x+16=0

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Solution for 12x^2-66x+16=0 equation: 


Simplifying
12x2 + -66x + 16 = 0

Reorder the terms:
16 + -66x + 12x2 = 0

Solving
16 + -66x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -33x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + -33x + 6x2)' equal to zero and attempt to solve:

Simplifying
8 + -33x + 6x2 = 0

Solving
8 + -33x + 6x2 = 0

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

Divide each side by '6'.
1.333333333 + -5.5x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -5.5x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -5.5x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -5.5x + x2 = 0 + -1.333333333
-5.5x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-5.5x + x2 = -1.333333333

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = -1.333333333 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = -1.333333333 + 7.5625

Combine like terms: -1.333333333 + 7.5625 = 6.229166667
7.5625 + -5.5x + x2 = 6.229166667

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 6.229166667

Calculate the square root of the right side: 2.495829855

Break this problem into two subproblems by setting 
(x + -2.75) equal to 2.495829855 and -2.495829855.


Subproblem 1
x + -2.75 = 2.495829855

Simplifying
x + -2.75 = 2.495829855

Reorder the terms:
-2.75 + x = 2.495829855

Solving
-2.75 + x = 2.495829855

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 2.495829855 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 2.495829855 + 2.75
x = 2.495829855 + 2.75

Combine like terms: 2.495829855 + 2.75 = 5.245829855
x = 5.245829855

Simplifying
x = 5.245829855


Subproblem 2
x + -2.75 = -2.495829855

Simplifying
x + -2.75 = -2.495829855

Reorder the terms:
-2.75 + x = -2.495829855

Solving
-2.75 + x = -2.495829855

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -2.495829855 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -2.495829855 + 2.75
x = -2.495829855 + 2.75

Combine like terms: -2.495829855 + 2.75 = 0.254170145
x = 0.254170145

Simplifying
x = 0.254170145


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.245829855, 0.254170145}
Solution
x = {5.245829855, 0.254170145}

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