3x^2=-x-2

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Solution for 3x^2=-x-2 equation: 


Simplifying
3x2 = -1x + -2

Reorder the terms:
3x2 = -2 + -1x

Solving
3x2 = -2 + -1x

Solving for variable 'x'.

Reorder the terms:
2 + x + 3x2 = -2 + -1x + 2 + x

Reorder the terms:
2 + x + 3x2 = -2 + 2 + -1x + x

Combine like terms: -2 + 2 = 0
2 + x + 3x2 = 0 + -1x + x
2 + x + 3x2 = -1x + x

Combine like terms: -1x + x = 0
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.

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