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Simplifying (x + y + 4) * dy + (x + -3y + -4) * dx = 0 Reorder the terms: (4 + x + y) * dy + (x + -3y + -4) * dx = 0 Reorder the terms for easier multiplication: dy(4 + x + y) + (x + -3y + -4) * dx = 0 (4 * dy + x * dy + y * dy) + (x + -3y + -4) * dx = 0 Reorder the terms: (dxy + 4dy + dy2) + (x + -3y + -4) * dx = 0 (dxy + 4dy + dy2) + (x + -3y + -4) * dx = 0 Reorder the terms: dxy + 4dy + dy2 + (-4 + x + -3y) * dx = 0 Reorder the terms for easier multiplication: dxy + 4dy + dy2 + dx(-4 + x + -3y) = 0 dxy + 4dy + dy2 + (-4 * dx + x * dx + -3y * dx) = 0 Reorder the terms: dxy + 4dy + dy2 + (-4dx + -3dxy + dx2) = 0 dxy + 4dy + dy2 + (-4dx + -3dxy + dx2) = 0 Reorder the terms: -4dx + dxy + -3dxy + dx2 + 4dy + dy2 = 0 Combine like terms: dxy + -3dxy = -2dxy -4dx + -2dxy + dx2 + 4dy + dy2 = 0 Solving -4dx + -2dxy + dx2 + 4dy + 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(-4x + -2xy + x2 + 4y + 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 '(-4x + -2xy + x2 + 4y + y2)' equal to zero and attempt to solve: Simplifying -4x + -2xy + x2 + 4y + y2 = 0 Solving -4x + -2xy + x2 + 4y + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '4x' to each side of the equation. -4x + -2xy + x2 + 4y + 4x + y2 = 0 + 4x Reorder the terms: -4x + 4x + -2xy + x2 + 4y + y2 = 0 + 4x Combine like terms: -4x + 4x = 0 0 + -2xy + x2 + 4y + y2 = 0 + 4x -2xy + x2 + 4y + y2 = 0 + 4x Remove the zero: -2xy + x2 + 4y + y2 = 4x Add '2xy' to each side of the equation. -2xy + x2 + 4y + 2xy + y2 = 4x + 2xy Reorder the terms: -2xy + 2xy + x2 + 4y + y2 = 4x + 2xy Combine like terms: -2xy + 2xy = 0 0 + x2 + 4y + y2 = 4x + 2xy x2 + 4y + y2 = 4x + 2xy Add '-1x2' to each side of the equation. x2 + 4y + -1x2 + y2 = 4x + 2xy + -1x2 Reorder the terms: x2 + -1x2 + 4y + y2 = 4x + 2xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 4y + y2 = 4x + 2xy + -1x2 4y + y2 = 4x + 2xy + -1x2 Add '-4y' to each side of the equation. 4y + -4y + y2 = 4x + 2xy + -1x2 + -4y Combine like terms: 4y + -4y = 0 0 + y2 = 4x + 2xy + -1x2 + -4y y2 = 4x + 2xy + -1x2 + -4y Add '-1y2' to each side of the equation. y2 + -1y2 = 4x + 2xy + -1x2 + -4y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = 4x + 2xy + -1x2 + -4y + -1y2 Simplifying 0 = 4x + 2xy + -1x2 + -4y + -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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