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Simplifying 3x2 + 2y2 + 3xy = 0 Reorder the terms: 3xy + 3x2 + 2y2 = 0 Solving 3xy + 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'. xy + x2 + 0.6666666667y2 = 0 Move the constant term to the right: Add '-0.6666666667y2' to each side of the equation. xy + x2 + 0.6666666667y2 + -0.6666666667y2 = 0 + -0.6666666667y2 Combine like terms: 0.6666666667y2 + -0.6666666667y2 = 0.0000000000 xy + x2 + 0.0000000000 = 0 + -0.6666666667y2 xy + x2 = 0 + -0.6666666667y2 Remove the zero: xy + 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. y2 + x2 + 0.25y2 = -0.6666666667y2 + 0.25y2 Reorder the terms: x2 + y2 + 0.25y2 = -0.6666666667y2 + 0.25y2 Combine like terms: y2 + 0.25y2 = 1.25y2 x2 + 1.25y2 = -0.6666666667y2 + 0.25y2 Combine like terms: -0.6666666667y2 + 0.25y2 = -0.4166666667y2 x2 + 1.25y2 = -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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