3x^2+xy+2y^2=0

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Solution for 3x^2+xy+2y^2=0 equation:


Simplifying
3x2 + xy + 2y2 = 0

Reorder the terms:
xy + 3x2 + 2y2 = 0

Solving
xy + 3x2 + 2y2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
0.3333333333xy + x2 + 0.6666666667y2 = 0

Move the constant term to the right:

Add '-0.6666666667y2' to each side of the equation.
0.3333333333xy + x2 + 0.6666666667y2 + -0.6666666667y2 = 0 + -0.6666666667y2

Combine like terms: 0.6666666667y2 + -0.6666666667y2 = 0.0000000000
0.3333333333xy + x2 + 0.0000000000 = 0 + -0.6666666667y2
0.3333333333xy + x2 = 0 + -0.6666666667y2
Remove the zero:
0.3333333333xy + x2 = -0.6666666667y2

The x term is xy.  Take half its coefficient (0.5y).
Square it (0.25y2) and add it to both sides.

Add '0.25y2' to each side of the equation.
0.3333333333xy + x2 + 0.25y2 = -0.6666666667y2 + 0.25y2

Combine like terms: -0.6666666667y2 + 0.25y2 = -0.4166666667y2
0.3333333333xy + x2 + 0.25y2 = -0.4166666667y2

Factor a perfect square on the left side:
(x + 0.5y)(x + 0.5y) = -0.4166666667y2

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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