-6x^2-14x-52=0

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Solution for -6x^2-14x-52=0 equation: 


Simplifying
-6x2 + -14x + -52 = 0

Reorder the terms:
-52 + -14x + -6x2 = 0

Solving
-52 + -14x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(26 + 7x + 3x2) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(26 + 7x + 3x2)' equal to zero and attempt to solve:

Simplifying
26 + 7x + 3x2 = 0

Solving
26 + 7x + 3x2 = 0

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

Divide each side by '3'.
8.666666667 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '-8.666666667' to each side of the equation.
8.666666667 + 2.333333333x + -8.666666667 + x2 = 0 + -8.666666667

Reorder the terms:
8.666666667 + -8.666666667 + 2.333333333x + x2 = 0 + -8.666666667

Combine like terms: 8.666666667 + -8.666666667 = 0.000000000
0.000000000 + 2.333333333x + x2 = 0 + -8.666666667
2.333333333x + x2 = 0 + -8.666666667

Combine like terms: 0 + -8.666666667 = -8.666666667
2.333333333x + x2 = -8.666666667

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = -8.666666667 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = -8.666666667 + 1.361111112

Combine like terms: -8.666666667 + 1.361111112 = -7.305555555
1.361111112 + 2.333333333x + x2 = -7.305555555

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = -7.305555555

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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