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Simplifying (xy + 4x) * dy + (x + 4y) * dx = 0 Reorder the terms: (4x + xy) * dy + (x + 4y) * dx = 0 Reorder the terms for easier multiplication: dy(4x + xy) + (x + 4y) * dx = 0 (4x * dy + xy * dy) + (x + 4y) * dx = 0 (4dxy + dxy2) + (x + 4y) * dx = 0 Reorder the terms for easier multiplication: 4dxy + dxy2 + dx(x + 4y) = 0 4dxy + dxy2 + (x * dx + 4y * dx) = 0 Reorder the terms: 4dxy + dxy2 + (4dxy + dx2) = 0 4dxy + dxy2 + (4dxy + dx2) = 0 Reorder the terms: 4dxy + 4dxy + dxy2 + dx2 = 0 Combine like terms: 4dxy + 4dxy = 8dxy 8dxy + dxy2 + dx2 = 0 Solving 8dxy + dxy2 + dx2 = 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(8y + y2 + x) = 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 '(8y + y2 + x)' equal to zero and attempt to solve: Simplifying 8y + y2 + x = 0 Reorder the terms: x + 8y + y2 = 0 Solving x + 8y + 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 + 8y + -1x + y2 = 0 + -1x Reorder the terms: x + -1x + 8y + y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + 8y + y2 = 0 + -1x 8y + y2 = 0 + -1x Remove the zero: 8y + y2 = -1x Add '-8y' to each side of the equation. 8y + -8y + y2 = -1x + -8y Combine like terms: 8y + -8y = 0 0 + y2 = -1x + -8y y2 = -1x + -8y Add '-1y2' to each side of the equation. y2 + -1y2 = -1x + -8y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -1x + -8y + -1y2 Simplifying 0 = -1x + -8y + -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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