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Simplifying (2x2 + -2y) * dy + -1(4xy + y2) * dx = 0 Reorder the terms for easier multiplication: dy(2x2 + -2y) + -1(4xy + y2) * dx = 0 (2x2 * dy + -2y * dy) + -1(4xy + y2) * dx = 0 (2dx2y + -2dy2) + -1(4xy + y2) * dx = 0 Reorder the terms for easier multiplication: 2dx2y + -2dy2 + -1dx(4xy + y2) = 0 2dx2y + -2dy2 + (4xy * -1dx + y2 * -1dx) = 0 Reorder the terms: 2dx2y + -2dy2 + (-1dxy2 + -4dx2y) = 0 2dx2y + -2dy2 + (-1dxy2 + -4dx2y) = 0 Reorder the terms: -1dxy2 + 2dx2y + -4dx2y + -2dy2 = 0 Combine like terms: 2dx2y + -4dx2y = -2dx2y -1dxy2 + -2dx2y + -2dy2 = 0 Solving -1dxy2 + -2dx2y + -2dy2 = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '-1dy'. -1dy(xy + 2x2 + 2y) = 0 Ignore the factor -1.Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve: Simplifying dy = 0 Solving dy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(xy + 2x2 + 2y)' equal to zero and attempt to solve: Simplifying xy + 2x2 + 2y = 0 Solving xy + 2x2 + 2y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1xy' to each side of the equation. xy + 2x2 + -1xy + 2y = 0 + -1xy Reorder the terms: xy + -1xy + 2x2 + 2y = 0 + -1xy Combine like terms: xy + -1xy = 0 0 + 2x2 + 2y = 0 + -1xy 2x2 + 2y = 0 + -1xy Remove the zero: 2x2 + 2y = -1xy Add '-2x2' to each side of the equation. 2x2 + -2x2 + 2y = -1xy + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + 2y = -1xy + -2x2 2y = -1xy + -2x2 Add '-2y' to each side of the equation. 2y + -2y = -1xy + -2x2 + -2y Combine like terms: 2y + -2y = 0 0 = -1xy + -2x2 + -2y Simplifying 0 = -1xy + -2x2 + -2y 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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