12x^2+6x+82=0

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Solution for 12x^2+6x+82=0 equation:


Simplifying
12x2 + 6x + 82 = 0

Reorder the terms:
82 + 6x + 12x2 = 0

Solving
82 + 6x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(41 + 3x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(41 + 3x + 6x2)' equal to zero and attempt to solve:

Simplifying
41 + 3x + 6x2 = 0

Solving
41 + 3x + 6x2 = 0

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

Divide each side by '6'.
6.833333333 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-6.833333333' to each side of the equation.
6.833333333 + 0.5x + -6.833333333 + x2 = 0 + -6.833333333

Reorder the terms:
6.833333333 + -6.833333333 + 0.5x + x2 = 0 + -6.833333333

Combine like terms: 6.833333333 + -6.833333333 = 0.000000000
0.000000000 + 0.5x + x2 = 0 + -6.833333333
0.5x + x2 = 0 + -6.833333333

Combine like terms: 0 + -6.833333333 = -6.833333333
0.5x + x2 = -6.833333333

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = -6.833333333 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = -6.833333333 + 0.0625

Combine like terms: -6.833333333 + 0.0625 = -6.770833333
0.0625 + 0.5x + x2 = -6.770833333

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = -6.770833333

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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