6x^2-4x+14=0

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Solution for 6x^2-4x+14=0 equation: 


Simplifying
6x2 + -4x + 14 = 0

Reorder the terms:
14 + -4x + 6x2 = 0

Solving
14 + -4x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -2x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + -2x + 3x2)' equal to zero and attempt to solve:

Simplifying
7 + -2x + 3x2 = 0

Solving
7 + -2x + 3x2 = 0

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

Divide each side by '3'.
2.333333333 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -0.6666666667x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -0.6666666667x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -0.6666666667x + x2 = 0 + -2.333333333
-0.6666666667x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-0.6666666667x + x2 = -2.333333333

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = -2.333333333 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = -2.333333333 + 0.1111111112

Combine like terms: -2.333333333 + 0.1111111112 = -2.2222222218
0.1111111112 + -0.6666666667x + x2 = -2.2222222218

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = -2.2222222218

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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