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Simplifying x(y + 1) * dy = (1 + -1y2) * dx Reorder the terms: x(1 + y) * dy = (1 + -1y2) * dx Reorder the terms for easier multiplication: x * dy(1 + y) = (1 + -1y2) * dx Multiply x * dy dxy(1 + y) = (1 + -1y2) * dx (1 * dxy + y * dxy) = (1 + -1y2) * dx (1dxy + dxy2) = (1 + -1y2) * dx Reorder the terms for easier multiplication: 1dxy + dxy2 = dx(1 + -1y2) 1dxy + dxy2 = (1 * dx + -1y2 * dx) 1dxy + dxy2 = (1dx + -1dxy2) Solving 1dxy + dxy2 = 1dx + -1dxy2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1dx' to each side of the equation. 1dxy + -1dx + dxy2 = 1dx + -1dx + -1dxy2 Reorder the terms: -1dx + 1dxy + dxy2 = 1dx + -1dx + -1dxy2 Combine like terms: 1dx + -1dx = 0 -1dx + 1dxy + dxy2 = 0 + -1dxy2 -1dx + 1dxy + dxy2 = -1dxy2 Add 'dxy2' to each side of the equation. -1dx + 1dxy + dxy2 + dxy2 = -1dxy2 + dxy2 Combine like terms: dxy2 + dxy2 = 2dxy2 -1dx + 1dxy + 2dxy2 = -1dxy2 + dxy2 Combine like terms: -1dxy2 + dxy2 = 0 -1dx + 1dxy + 2dxy2 = 0 Factor out the Greatest Common Factor (GCF), 'dx'. dx(-1 + y + 2y2) = 0 Factor a trinomial. dx((-1 + -1y)(1 + -2y)) = 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 '(-1 + -1y)' equal to zero and attempt to solve: Simplifying -1 + -1y = 0 Solving -1 + -1y = 0 Move all terms containing d to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1y = 0 + 1 -1y = 0 + 1 Combine like terms: 0 + 1 = 1 -1y = 1 Add 'y' to each side of the equation. -1y + y = 1 + y Combine like terms: -1y + y = 0 0 = 1 + y Simplifying 0 = 1 + y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + -2y)' equal to zero and attempt to solve: Simplifying 1 + -2y = 0 Solving 1 + -2y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2y = 0 + -1 -2y = 0 + -1 Combine like terms: 0 + -1 = -1 -2y = -1 Add '2y' to each side of the equation. -2y + 2y = -1 + 2y Combine like terms: -2y + 2y = 0 0 = -1 + 2y Simplifying 0 = -1 + 2y 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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