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Simplifying 2y(x + y + 2) * dx = (x2 + 4x + -1y2 + 1) * dy Reorder the terms: 2y(2 + x + y) * dx = (x2 + 4x + -1y2 + 1) * dy Reorder the terms for easier multiplication: 2y * dx(2 + x + y) = (x2 + 4x + -1y2 + 1) * dy Multiply y * dx 2dxy(2 + x + y) = (x2 + 4x + -1y2 + 1) * dy (2 * 2dxy + x * 2dxy + y * 2dxy) = (x2 + 4x + -1y2 + 1) * dy Reorder the terms: (4dxy + 2dxy2 + 2dx2y) = (x2 + 4x + -1y2 + 1) * dy (4dxy + 2dxy2 + 2dx2y) = (x2 + 4x + -1y2 + 1) * dy Reorder the terms: 4dxy + 2dxy2 + 2dx2y = (1 + 4x + x2 + -1y2) * dy Reorder the terms for easier multiplication: 4dxy + 2dxy2 + 2dx2y = dy(1 + 4x + x2 + -1y2) 4dxy + 2dxy2 + 2dx2y = (1 * dy + 4x * dy + x2 * dy + -1y2 * dy) Reorder the terms: 4dxy + 2dxy2 + 2dx2y = (4dxy + dx2y + 1dy + -1dy3) 4dxy + 2dxy2 + 2dx2y = (4dxy + dx2y + 1dy + -1dy3) Add '-4dxy' to each side of the equation. 4dxy + 2dxy2 + -4dxy + 2dx2y = 4dxy + dx2y + 1dy + -4dxy + -1dy3 Reorder the terms: 4dxy + -4dxy + 2dxy2 + 2dx2y = 4dxy + dx2y + 1dy + -4dxy + -1dy3 Combine like terms: 4dxy + -4dxy = 0 0 + 2dxy2 + 2dx2y = 4dxy + dx2y + 1dy + -4dxy + -1dy3 2dxy2 + 2dx2y = 4dxy + dx2y + 1dy + -4dxy + -1dy3 Reorder the terms: 2dxy2 + 2dx2y = 4dxy + -4dxy + dx2y + 1dy + -1dy3 Combine like terms: 4dxy + -4dxy = 0 2dxy2 + 2dx2y = 0 + dx2y + 1dy + -1dy3 2dxy2 + 2dx2y = dx2y + 1dy + -1dy3 Solving 2dxy2 + 2dx2y = dx2y + 1dy + -1dy3 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1dx2y' to each side of the equation. 2dxy2 + 2dx2y + -1dx2y = dx2y + 1dy + -1dx2y + -1dy3 Combine like terms: 2dx2y + -1dx2y = 1dx2y 2dxy2 + 1dx2y = dx2y + 1dy + -1dx2y + -1dy3 Reorder the terms: 2dxy2 + 1dx2y = dx2y + -1dx2y + 1dy + -1dy3 Combine like terms: dx2y + -1dx2y = 0 2dxy2 + 1dx2y = 0 + 1dy + -1dy3 2dxy2 + 1dx2y = 1dy + -1dy3 Add '-1dy' to each side of the equation. 2dxy2 + 1dx2y + -1dy = 1dy + -1dy + -1dy3 Combine like terms: 1dy + -1dy = 0 2dxy2 + 1dx2y + -1dy = 0 + -1dy3 2dxy2 + 1dx2y + -1dy = -1dy3 Add 'dy3' to each side of the equation. 2dxy2 + 1dx2y + -1dy + dy3 = -1dy3 + dy3 Combine like terms: -1dy3 + dy3 = 0 2dxy2 + 1dx2y + -1dy + dy3 = 0 Factor out the Greatest Common Factor (GCF), 'dy'. dy(2xy + x2 + -1 + y2) = 0Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve: Simplifying dy = 0 Solving dy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy = 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 '(2xy + x2 + -1 + y2)' equal to zero and attempt to solve: Simplifying 2xy + x2 + -1 + y2 = 0 Reorder the terms: -1 + 2xy + x2 + y2 = 0 Solving -1 + 2xy + x2 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 2xy + x2 + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + 2xy + x2 + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2xy + x2 + y2 = 0 + 1 2xy + x2 + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 2xy + x2 + y2 = 1 Add '-2xy' to each side of the equation. 2xy + x2 + -2xy + y2 = 1 + -2xy Reorder the terms: 2xy + -2xy + x2 + y2 = 1 + -2xy Combine like terms: 2xy + -2xy = 0 0 + x2 + y2 = 1 + -2xy x2 + y2 = 1 + -2xy Add '-1x2' to each side of the equation. x2 + -1x2 + y2 = 1 + -2xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + y2 = 1 + -2xy + -1x2 y2 = 1 + -2xy + -1x2 Add '-1y2' to each side of the equation. y2 + -1y2 = 1 + -2xy + -1x2 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = 1 + -2xy + -1x2 + -1y2 Simplifying 0 = 1 + -2xy + -1x2 + -1y2 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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