6x^2+8x+14=0

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Solution for 6x^2+8x+14=0 equation: 


Simplifying
6x2 + 8x + 14 = 0

Reorder the terms:
14 + 8x + 6x2 = 0

Solving
14 + 8x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 4x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + 4x + 3x2)' equal to zero and attempt to solve:

Simplifying
7 + 4x + 3x2 = 0

Solving
7 + 4x + 3x2 = 0

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

Divide each side by '3'.
2.333333333 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + 1.333333333x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + 1.333333333x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + 1.333333333x + x2 = 0 + -2.333333333
1.333333333x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
1.333333333x + x2 = -2.333333333

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = -2.333333333 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = -2.333333333 + 0.4444444442

Combine like terms: -2.333333333 + 0.4444444442 = -1.8888888888
0.4444444442 + 1.333333333x + x2 = -1.8888888888

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = -1.8888888888

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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