-6x^2-2x-28=0

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


Simplifying
-6x2 + -2x + -28 = 0

Reorder the terms:
-28 + -2x + -6x2 = 0

Solving
-28 + -2x + -6x2 = 0

Solving for variable 'x'.

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

Ignore the factor -2.

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

Simplifying
14 + x + 3x2 = 0

Solving
14 + x + 3x2 = 0

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

Divide each side by '3'.
4.666666667 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-4.666666667' to each side of the equation.
4.666666667 + 0.3333333333x + -4.666666667 + x2 = 0 + -4.666666667

Reorder the terms:
4.666666667 + -4.666666667 + 0.3333333333x + x2 = 0 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + 0.3333333333x + x2 = 0 + -4.666666667
0.3333333333x + x2 = 0 + -4.666666667

Combine like terms: 0 + -4.666666667 = -4.666666667
0.3333333333x + x2 = -4.666666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.3333333333x + 0.25 + x2 = -4.666666667 + 0.25

Reorder the terms:
0.25 + 0.3333333333x + x2 = -4.666666667 + 0.25

Combine like terms: -4.666666667 + 0.25 = -4.416666667
0.25 + 0.3333333333x + x2 = -4.416666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -4.416666667

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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