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Simplifying (x + xy) * dx + (y + xy) * dy = 0 Reorder the terms for easier multiplication: dx(x + xy) + (y + xy) * dy = 0 (x * dx + xy * dx) + (y + xy) * dy = 0 (dx2 + dx2y) + (y + xy) * dy = 0 Reorder the terms: dx2 + dx2y + (xy + y) * dy = 0 Reorder the terms for easier multiplication: dx2 + dx2y + dy(xy + y) = 0 dx2 + dx2y + (xy * dy + y * dy) = 0 dx2 + dx2y + (dxy2 + dy2) = 0 Reorder the terms: dxy2 + dx2 + dx2y + dy2 = 0 Solving dxy2 + dx2 + dx2y + dy2 = 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), 'd'. d(xy2 + x2 + x2y + y2) = 0Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(xy2 + x2 + x2y + y2)' equal to zero and attempt to solve: Simplifying xy2 + x2 + x2y + y2 = 0 Solving xy2 + x2 + x2y + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1xy2' to each side of the equation. xy2 + x2 + x2y + -1xy2 + y2 = 0 + -1xy2 Reorder the terms: xy2 + -1xy2 + x2 + x2y + y2 = 0 + -1xy2 Combine like terms: xy2 + -1xy2 = 0 0 + x2 + x2y + y2 = 0 + -1xy2 x2 + x2y + y2 = 0 + -1xy2 Remove the zero: x2 + x2y + y2 = -1xy2 Add '-1x2' to each side of the equation. x2 + x2y + -1x2 + y2 = -1xy2 + -1x2 Reorder the terms: x2 + -1x2 + x2y + y2 = -1xy2 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + x2y + y2 = -1xy2 + -1x2 x2y + y2 = -1xy2 + -1x2 Add '-1x2y' to each side of the equation. x2y + -1x2y + y2 = -1xy2 + -1x2 + -1x2y Combine like terms: x2y + -1x2y = 0 0 + y2 = -1xy2 + -1x2 + -1x2y y2 = -1xy2 + -1x2 + -1x2y Add '-1y2' to each side of the equation. y2 + -1y2 = -1xy2 + -1x2 + -1x2y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -1xy2 + -1x2 + -1x2y + -1y2 Simplifying 0 = -1xy2 + -1x2 + -1x2y + -1y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
d = {0}
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