6x^2-20x+234=0

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Solution for 6x^2-20x+234=0 equation: 


Simplifying
6x2 + -20x + 234 = 0

Reorder the terms:
234 + -20x + 6x2 = 0

Solving
234 + -20x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(117 + -10x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(117 + -10x + 3x2)' equal to zero and attempt to solve:

Simplifying
117 + -10x + 3x2 = 0

Solving
117 + -10x + 3x2 = 0

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

Divide each side by '3'.
39 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '-39' to each side of the equation.
39 + -3.333333333x + -39 + x2 = 0 + -39

Reorder the terms:
39 + -39 + -3.333333333x + x2 = 0 + -39

Combine like terms: 39 + -39 = 0
0 + -3.333333333x + x2 = 0 + -39
-3.333333333x + x2 = 0 + -39

Combine like terms: 0 + -39 = -39
-3.333333333x + x2 = -39

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = -39 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = -39 + 2.777777779

Combine like terms: -39 + 2.777777779 = -36.222222221
2.777777779 + -3.333333333x + x2 = -36.222222221

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = -36.222222221

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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