6x^2+16x+56=0

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Solution for 6x^2+16x+56=0 equation: 


Simplifying
6x2 + 16x + 56 = 0

Reorder the terms:
56 + 16x + 6x2 = 0

Solving
56 + 16x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(28 + 8x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(28 + 8x + 3x2)' equal to zero and attempt to solve:

Simplifying
28 + 8x + 3x2 = 0

Solving
28 + 8x + 3x2 = 0

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

Divide each side by '3'.
9.333333333 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '-9.333333333' to each side of the equation.
9.333333333 + 2.666666667x + -9.333333333 + x2 = 0 + -9.333333333

Reorder the terms:
9.333333333 + -9.333333333 + 2.666666667x + x2 = 0 + -9.333333333

Combine like terms: 9.333333333 + -9.333333333 = 0.000000000
0.000000000 + 2.666666667x + x2 = 0 + -9.333333333
2.666666667x + x2 = 0 + -9.333333333

Combine like terms: 0 + -9.333333333 = -9.333333333
2.666666667x + x2 = -9.333333333

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = -9.333333333 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = -9.333333333 + 1.777777780

Combine like terms: -9.333333333 + 1.777777780 = -7.555555553
1.777777780 + 2.666666667x + x2 = -7.555555553

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = -7.555555553

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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