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Simplifying (x + y + -2) * dx + (x + -1y + 4) * dy = 0 Reorder the terms: (-2 + x + y) * dx + (x + -1y + 4) * dy = 0 Reorder the terms for easier multiplication: dx(-2 + x + y) + (x + -1y + 4) * dy = 0 (-2 * dx + x * dx + y * dx) + (x + -1y + 4) * dy = 0 Reorder the terms: (-2dx + dxy + dx2) + (x + -1y + 4) * dy = 0 (-2dx + dxy + dx2) + (x + -1y + 4) * dy = 0 Reorder the terms: -2dx + dxy + dx2 + (4 + x + -1y) * dy = 0 Reorder the terms for easier multiplication: -2dx + dxy + dx2 + dy(4 + x + -1y) = 0 -2dx + dxy + dx2 + (4 * dy + x * dy + -1y * dy) = 0 Reorder the terms: -2dx + dxy + dx2 + (dxy + 4dy + -1dy2) = 0 -2dx + dxy + dx2 + (dxy + 4dy + -1dy2) = 0 Reorder the terms: -2dx + dxy + dxy + dx2 + 4dy + -1dy2 = 0 Combine like terms: dxy + dxy = 2dxy -2dx + 2dxy + dx2 + 4dy + -1dy2 = 0 Solving -2dx + 2dxy + dx2 + 4dy + -1dy2 = 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(-2x + 2xy + x2 + 4y + -1y2) = 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 '(-2x + 2xy + x2 + 4y + -1y2)' equal to zero and attempt to solve: Simplifying -2x + 2xy + x2 + 4y + -1y2 = 0 Solving -2x + 2xy + x2 + 4y + -1y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '2x' to each side of the equation. -2x + 2xy + x2 + 4y + 2x + -1y2 = 0 + 2x Reorder the terms: -2x + 2x + 2xy + x2 + 4y + -1y2 = 0 + 2x Combine like terms: -2x + 2x = 0 0 + 2xy + x2 + 4y + -1y2 = 0 + 2x 2xy + x2 + 4y + -1y2 = 0 + 2x Remove the zero: 2xy + x2 + 4y + -1y2 = 2x Add '-2xy' to each side of the equation. 2xy + x2 + 4y + -2xy + -1y2 = 2x + -2xy Reorder the terms: 2xy + -2xy + x2 + 4y + -1y2 = 2x + -2xy Combine like terms: 2xy + -2xy = 0 0 + x2 + 4y + -1y2 = 2x + -2xy x2 + 4y + -1y2 = 2x + -2xy Add '-1x2' to each side of the equation. x2 + 4y + -1x2 + -1y2 = 2x + -2xy + -1x2 Reorder the terms: x2 + -1x2 + 4y + -1y2 = 2x + -2xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 4y + -1y2 = 2x + -2xy + -1x2 4y + -1y2 = 2x + -2xy + -1x2 Add '-4y' to each side of the equation. 4y + -4y + -1y2 = 2x + -2xy + -1x2 + -4y Combine like terms: 4y + -4y = 0 0 + -1y2 = 2x + -2xy + -1x2 + -4y -1y2 = 2x + -2xy + -1x2 + -4y Add 'y2' to each side of the equation. -1y2 + y2 = 2x + -2xy + -1x2 + -4y + y2 Combine like terms: -1y2 + y2 = 0 0 = 2x + -2xy + -1x2 + -4y + y2 Simplifying 0 = 2x + -2xy + -1x2 + -4y + y2 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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