9x^2+3x=-6

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Solution for 9x^2+3x=-6 equation: 


Simplifying
9x2 + 3x = -6

Reorder the terms:
3x + 9x2 = -6

Solving
3x + 9x2 = -6

Solving for variable 'x'.

Reorder the terms:
6 + 3x + 9x2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 3x + 9x2 = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(2 + x + 3x2)' equal to zero and attempt to solve:

Simplifying
2 + x + 3x2 = 0

Solving
2 + x + 3x2 = 0

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

Divide each side by '3'.
0.6666666667 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 0.3333333333x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 0.3333333333x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 0.3333333333x + x2 = 0 + -0.6666666667
0.3333333333x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
0.3333333333x + x2 = -0.6666666667

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.
0.3333333333x + 0.25 + x2 = -0.6666666667 + 0.25

Reorder the terms:
0.25 + 0.3333333333x + x2 = -0.6666666667 + 0.25

Combine like terms: -0.6666666667 + 0.25 = -0.4166666667
0.25 + 0.3333333333x + x2 = -0.4166666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -0.4166666667

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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