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Simplifying (xy + x) * dx = (x2y2 + x2 + y2 + 1) * dy Reorder the terms: (x + xy) * dx = (x2y2 + x2 + y2 + 1) * dy Reorder the terms for easier multiplication: dx(x + xy) = (x2y2 + x2 + y2 + 1) * dy (x * dx + xy * dx) = (x2y2 + x2 + y2 + 1) * dy (dx2 + dx2y) = (x2y2 + x2 + y2 + 1) * dy Reorder the terms: dx2 + dx2y = (1 + x2 + x2y2 + y2) * dy Reorder the terms for easier multiplication: dx2 + dx2y = dy(1 + x2 + x2y2 + y2) dx2 + dx2y = (1 * dy + x2 * dy + x2y2 * dy + y2 * dy) Reorder the terms: dx2 + dx2y = (dx2y + dx2y3 + 1dy + dy3) dx2 + dx2y = (dx2y + dx2y3 + 1dy + dy3) Add '-1dx2y' to each side of the equation. dx2 + dx2y + -1dx2y = dx2y + dx2y3 + 1dy + -1dx2y + dy3 Combine like terms: dx2y + -1dx2y = 0 dx2 + 0 = dx2y + dx2y3 + 1dy + -1dx2y + dy3 dx2 = dx2y + dx2y3 + 1dy + -1dx2y + dy3 Reorder the terms: dx2 = dx2y + -1dx2y + dx2y3 + 1dy + dy3 Combine like terms: dx2y + -1dx2y = 0 dx2 = 0 + dx2y3 + 1dy + dy3 dx2 = dx2y3 + 1dy + dy3 Solving dx2 = dx2y3 + 1dy + dy3 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1dx2y3' to each side of the equation. dx2 + -1dx2y3 = dx2y3 + 1dy + -1dx2y3 + dy3 Reorder the terms: dx2 + -1dx2y3 = dx2y3 + -1dx2y3 + 1dy + dy3 Combine like terms: dx2y3 + -1dx2y3 = 0 dx2 + -1dx2y3 = 0 + 1dy + dy3 dx2 + -1dx2y3 = 1dy + dy3 Add '-1dy' to each side of the equation. dx2 + -1dx2y3 + -1dy = 1dy + -1dy + dy3 Combine like terms: 1dy + -1dy = 0 dx2 + -1dx2y3 + -1dy = 0 + dy3 dx2 + -1dx2y3 + -1dy = dy3 Add '-1dy3' to each side of the equation. dx2 + -1dx2y3 + -1dy + -1dy3 = dy3 + -1dy3 Combine like terms: dy3 + -1dy3 = 0 dx2 + -1dx2y3 + -1dy + -1dy3 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(x2 + -1x2y3 + -1y + -1y3) = 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 '(x2 + -1x2y3 + -1y + -1y3)' equal to zero and attempt to solve: Simplifying x2 + -1x2y3 + -1y + -1y3 = 0 Solving x2 + -1x2y3 + -1y + -1y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x2' to each side of the equation. x2 + -1x2y3 + -1y + -1x2 + -1y3 = 0 + -1x2 Reorder the terms: x2 + -1x2 + -1x2y3 + -1y + -1y3 = 0 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + -1x2y3 + -1y + -1y3 = 0 + -1x2 -1x2y3 + -1y + -1y3 = 0 + -1x2 Remove the zero: -1x2y3 + -1y + -1y3 = -1x2 Add 'x2y3' to each side of the equation. -1x2y3 + -1y + x2y3 + -1y3 = -1x2 + x2y3 Reorder the terms: -1x2y3 + x2y3 + -1y + -1y3 = -1x2 + x2y3 Combine like terms: -1x2y3 + x2y3 = 0 0 + -1y + -1y3 = -1x2 + x2y3 -1y + -1y3 = -1x2 + x2y3 Add 'y' to each side of the equation. -1y + y + -1y3 = -1x2 + x2y3 + y Combine like terms: -1y + y = 0 0 + -1y3 = -1x2 + x2y3 + y -1y3 = -1x2 + x2y3 + y Add 'y3' to each side of the equation. -1y3 + y3 = -1x2 + x2y3 + y + y3 Combine like terms: -1y3 + y3 = 0 0 = -1x2 + x2y3 + y + y3 Simplifying 0 = -1x2 + x2y3 + y + y3 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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