3q^2+4q=-2

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Solution for 3q^2+4q=-2 equation: 


Simplifying
3q2 + 4q = -2

Reorder the terms:
4q + 3q2 = -2

Solving
4q + 3q2 = -2

Solving for variable 'q'.

Reorder the terms:
2 + 4q + 3q2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + 4q + 3q2 = 0

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

Divide each side by '3'.
0.6666666667 + 1.333333333q + q2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 1.333333333q + -0.6666666667 + q2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 1.333333333q + q2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 1.333333333q + q2 = 0 + -0.6666666667
1.333333333q + q2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
1.333333333q + q2 = -0.6666666667

The q term is 1.333333333q.  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.
1.333333333q + 0.4444444442 + q2 = -0.6666666667 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333q + q2 = -0.6666666667 + 0.4444444442

Combine like terms: -0.6666666667 + 0.4444444442 = -0.2222222225
0.4444444442 + 1.333333333q + q2 = -0.2222222225

Factor a perfect square on the left side:
(q + 0.6666666665)(q + 0.6666666665) = -0.2222222225

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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