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