-6x^2-5x-14=0

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Solution for -6x^2-5x-14=0 equation: 


Simplifying
-6x2 + -5x + -14 = 0

Reorder the terms:
-14 + -5x + -6x2 = 0

Solving
-14 + -5x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(14 + 5x + 6x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(14 + 5x + 6x2)' equal to zero and attempt to solve:

Simplifying
14 + 5x + 6x2 = 0

Solving
14 + 5x + 6x2 = 0

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

Divide each side by '6'.
2.333333333 + 0.8333333333x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + 0.8333333333x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + 0.8333333333x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + 0.8333333333x + x2 = 0 + -2.333333333
0.8333333333x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
0.8333333333x + x2 = -2.333333333

The x term is 0.8333333333x.  Take half its coefficient (0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
0.8333333333x + 0.1736111111 + x2 = -2.333333333 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333333x + x2 = -2.333333333 + 0.1736111111

Combine like terms: -2.333333333 + 0.1736111111 = -2.1597222219
0.1736111111 + 0.8333333333x + x2 = -2.1597222219

Factor a perfect square on the left side:
(x + 0.4166666667)(x + 0.4166666667) = -2.1597222219

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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