6x^2-28x+130=0

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Solution for 6x^2-28x+130=0 equation: 


Simplifying
6x2 + -28x + 130 = 0

Reorder the terms:
130 + -28x + 6x2 = 0

Solving
130 + -28x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(65 + -14x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(65 + -14x + 3x2)' equal to zero and attempt to solve:

Simplifying
65 + -14x + 3x2 = 0

Solving
65 + -14x + 3x2 = 0

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

Divide each side by '3'.
21.66666667 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '-21.66666667' to each side of the equation.
21.66666667 + -4.666666667x + -21.66666667 + x2 = 0 + -21.66666667

Reorder the terms:
21.66666667 + -21.66666667 + -4.666666667x + x2 = 0 + -21.66666667

Combine like terms: 21.66666667 + -21.66666667 = 0.00000000
0.00000000 + -4.666666667x + x2 = 0 + -21.66666667
-4.666666667x + x2 = 0 + -21.66666667

Combine like terms: 0 + -21.66666667 = -21.66666667
-4.666666667x + x2 = -21.66666667

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = -21.66666667 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = -21.66666667 + 5.444444448

Combine like terms: -21.66666667 + 5.444444448 = -16.222222222
5.444444448 + -4.666666667x + x2 = -16.222222222

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = -16.222222222

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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