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Simplifying (x + y + 1) * dx = (2x + 2y + -1) * dy Reorder the terms: (1 + x + y) * dx = (2x + 2y + -1) * dy Reorder the terms for easier multiplication: dx(1 + x + y) = (2x + 2y + -1) * dy (1 * dx + x * dx + y * dx) = (2x + 2y + -1) * dy Reorder the terms: (1dx + dxy + dx2) = (2x + 2y + -1) * dy (1dx + dxy + dx2) = (2x + 2y + -1) * dy Reorder the terms: 1dx + dxy + dx2 = (-1 + 2x + 2y) * dy Reorder the terms for easier multiplication: 1dx + dxy + dx2 = dy(-1 + 2x + 2y) 1dx + dxy + dx2 = (-1 * dy + 2x * dy + 2y * dy) Reorder the terms: 1dx + dxy + dx2 = (2dxy + -1dy + 2dy2) 1dx + dxy + dx2 = (2dxy + -1dy + 2dy2) Solving 1dx + dxy + dx2 = 2dxy + -1dy + 2dy2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-2dxy' to each side of the equation. 1dx + dxy + -2dxy + dx2 = 2dxy + -1dy + -2dxy + 2dy2 Combine like terms: dxy + -2dxy = -1dxy 1dx + -1dxy + dx2 = 2dxy + -1dy + -2dxy + 2dy2 Reorder the terms: 1dx + -1dxy + dx2 = 2dxy + -2dxy + -1dy + 2dy2 Combine like terms: 2dxy + -2dxy = 0 1dx + -1dxy + dx2 = 0 + -1dy + 2dy2 1dx + -1dxy + dx2 = -1dy + 2dy2 Add 'dy' to each side of the equation. 1dx + -1dxy + dx2 + dy = -1dy + dy + 2dy2 Combine like terms: -1dy + dy = 0 1dx + -1dxy + dx2 + dy = 0 + 2dy2 1dx + -1dxy + dx2 + dy = 2dy2 Add '-2dy2' to each side of the equation. 1dx + -1dxy + dx2 + dy + -2dy2 = 2dy2 + -2dy2 Combine like terms: 2dy2 + -2dy2 = 0 1dx + -1dxy + dx2 + dy + -2dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(x + -1xy + x2 + y + -2y2) = 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 '(x + -1xy + x2 + y + -2y2)' equal to zero and attempt to solve: Simplifying x + -1xy + x2 + y + -2y2 = 0 Solving x + -1xy + x2 + y + -2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1xy + x2 + y + -1x + -2y2 = 0 + -1x Reorder the terms: x + -1x + -1xy + x2 + y + -2y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + -1xy + x2 + y + -2y2 = 0 + -1x -1xy + x2 + y + -2y2 = 0 + -1x Remove the zero: -1xy + x2 + y + -2y2 = -1x Add 'xy' to each side of the equation. -1xy + x2 + y + xy + -2y2 = -1x + xy Reorder the terms: -1xy + xy + x2 + y + -2y2 = -1x + xy Combine like terms: -1xy + xy = 0 0 + x2 + y + -2y2 = -1x + xy x2 + y + -2y2 = -1x + xy Add '-1x2' to each side of the equation. x2 + y + -1x2 + -2y2 = -1x + xy + -1x2 Reorder the terms: x2 + -1x2 + y + -2y2 = -1x + xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + y + -2y2 = -1x + xy + -1x2 y + -2y2 = -1x + xy + -1x2 Add '-1y' to each side of the equation. y + -1y + -2y2 = -1x + xy + -1x2 + -1y Combine like terms: y + -1y = 0 0 + -2y2 = -1x + xy + -1x2 + -1y -2y2 = -1x + xy + -1x2 + -1y Add '2y2' to each side of the equation. -2y2 + 2y2 = -1x + xy + -1x2 + -1y + 2y2 Combine like terms: -2y2 + 2y2 = 0 0 = -1x + xy + -1x2 + -1y + 2y2 Simplifying 0 = -1x + xy + -1x2 + -1y + 2y2 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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