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Simplifying (2x + -2y + -1x2 + 2xy) * dx + (2x2 + -4xy + -2x) * dy = 0 Reorder the terms: (2x + 2xy + -1x2 + -2y) * dx + (2x2 + -4xy + -2x) * dy = 0 Reorder the terms for easier multiplication: dx(2x + 2xy + -1x2 + -2y) + (2x2 + -4xy + -2x) * dy = 0 (2x * dx + 2xy * dx + -1x2 * dx + -2y * dx) + (2x2 + -4xy + -2x) * dy = 0 Reorder the terms: (-2dxy + 2dx2 + 2dx2y + -1dx3) + (2x2 + -4xy + -2x) * dy = 0 (-2dxy + 2dx2 + 2dx2y + -1dx3) + (2x2 + -4xy + -2x) * dy = 0 Reorder the terms: -2dxy + 2dx2 + 2dx2y + -1dx3 + (-2x + -4xy + 2x2) * dy = 0 Reorder the terms for easier multiplication: -2dxy + 2dx2 + 2dx2y + -1dx3 + dy(-2x + -4xy + 2x2) = 0 -2dxy + 2dx2 + 2dx2y + -1dx3 + (-2x * dy + -4xy * dy + 2x2 * dy) = 0 -2dxy + 2dx2 + 2dx2y + -1dx3 + (-2dxy + -4dxy2 + 2dx2y) = 0 Reorder the terms: -2dxy + -2dxy + -4dxy2 + 2dx2 + 2dx2y + 2dx2y + -1dx3 = 0 Combine like terms: -2dxy + -2dxy = -4dxy -4dxy + -4dxy2 + 2dx2 + 2dx2y + 2dx2y + -1dx3 = 0 Combine like terms: 2dx2y + 2dx2y = 4dx2y -4dxy + -4dxy2 + 2dx2 + 4dx2y + -1dx3 = 0 Solving -4dxy + -4dxy2 + 2dx2 + 4dx2y + -1dx3 = 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), 'dx'. dx(-4y + -4y2 + 2x + 4xy + -1x2) = 0Subproblem 1
Set the factor 'dx' equal to zero and attempt to solve: Simplifying dx = 0 Solving dx = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-4y + -4y2 + 2x + 4xy + -1x2)' equal to zero and attempt to solve: Simplifying -4y + -4y2 + 2x + 4xy + -1x2 = 0 Reorder the terms: 2x + 4xy + -1x2 + -4y + -4y2 = 0 Solving 2x + 4xy + -1x2 + -4y + -4y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x' to each side of the equation. 2x + 4xy + -1x2 + -4y + -2x + -4y2 = 0 + -2x Reorder the terms: 2x + -2x + 4xy + -1x2 + -4y + -4y2 = 0 + -2x Combine like terms: 2x + -2x = 0 0 + 4xy + -1x2 + -4y + -4y2 = 0 + -2x 4xy + -1x2 + -4y + -4y2 = 0 + -2x Remove the zero: 4xy + -1x2 + -4y + -4y2 = -2x Add '-4xy' to each side of the equation. 4xy + -1x2 + -4y + -4xy + -4y2 = -2x + -4xy Reorder the terms: 4xy + -4xy + -1x2 + -4y + -4y2 = -2x + -4xy Combine like terms: 4xy + -4xy = 0 0 + -1x2 + -4y + -4y2 = -2x + -4xy -1x2 + -4y + -4y2 = -2x + -4xy Add 'x2' to each side of the equation. -1x2 + -4y + x2 + -4y2 = -2x + -4xy + x2 Reorder the terms: -1x2 + x2 + -4y + -4y2 = -2x + -4xy + x2 Combine like terms: -1x2 + x2 = 0 0 + -4y + -4y2 = -2x + -4xy + x2 -4y + -4y2 = -2x + -4xy + x2 Add '4y' to each side of the equation. -4y + 4y + -4y2 = -2x + -4xy + x2 + 4y Combine like terms: -4y + 4y = 0 0 + -4y2 = -2x + -4xy + x2 + 4y -4y2 = -2x + -4xy + x2 + 4y Add '4y2' to each side of the equation. -4y2 + 4y2 = -2x + -4xy + x2 + 4y + 4y2 Combine like terms: -4y2 + 4y2 = 0 0 = -2x + -4xy + x2 + 4y + 4y2 Simplifying 0 = -2x + -4xy + x2 + 4y + 4y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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