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