12x^2+2x+34=6

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Solution for 12x^2+2x+34=6 equation:


Simplifying
12x2 + 2x + 34 = 6

Reorder the terms:
34 + 2x + 12x2 = 6

Solving
34 + 2x + 12x2 = 6

Solving for variable 'x'.

Reorder the terms:
34 + -6 + 2x + 12x2 = 6 + -6

Combine like terms: 34 + -6 = 28
28 + 2x + 12x2 = 6 + -6

Combine like terms: 6 + -6 = 0
28 + 2x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + x + 6x2) = 0

Ignore the factor 2.

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

Simplifying
14 + x + 6x2 = 0

Solving
14 + x + 6x2 = 0

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

Divide each side by '6'.
2.333333333 + 0.1666666667x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + 0.1666666667x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + 0.1666666667x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + 0.1666666667x + x2 = 0 + -2.333333333
0.1666666667x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
0.1666666667x + x2 = -2.333333333

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

Add '0.25' to each side of the equation.
0.1666666667x + 0.25 + x2 = -2.333333333 + 0.25

Reorder the terms:
0.25 + 0.1666666667x + x2 = -2.333333333 + 0.25

Combine like terms: -2.333333333 + 0.25 = -2.083333333
0.25 + 0.1666666667x + x2 = -2.083333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -2.083333333

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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