12x^2-44x+126=0

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Solution for 12x^2-44x+126=0 equation: 


Simplifying
12x2 + -44x + 126 = 0

Reorder the terms:
126 + -44x + 12x2 = 0

Solving
126 + -44x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(63 + -22x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(63 + -22x + 6x2)' equal to zero and attempt to solve:

Simplifying
63 + -22x + 6x2 = 0

Solving
63 + -22x + 6x2 = 0

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

Divide each side by '6'.
10.5 + -3.666666667x + x2 = 0

Move the constant term to the right:

Add '-10.5' to each side of the equation.
10.5 + -3.666666667x + -10.5 + x2 = 0 + -10.5

Reorder the terms:
10.5 + -10.5 + -3.666666667x + x2 = 0 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + -3.666666667x + x2 = 0 + -10.5
-3.666666667x + x2 = 0 + -10.5

Combine like terms: 0 + -10.5 = -10.5
-3.666666667x + x2 = -10.5

The x term is -3.666666667x.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667x + 3.361111114 + x2 = -10.5 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667x + x2 = -10.5 + 3.361111114

Combine like terms: -10.5 + 3.361111114 = -7.138888886
3.361111114 + -3.666666667x + x2 = -7.138888886

Factor a perfect square on the left side:
(x + -1.833333334)(x + -1.833333334) = -7.138888886

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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