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Simplifying (xy + 1) * dx + x(x + 4y + -2) * dy = 0 Reorder the terms: (1 + xy) * dx + x(x + 4y + -2) * dy = 0 Reorder the terms for easier multiplication: dx(1 + xy) + x(x + 4y + -2) * dy = 0 (1 * dx + xy * dx) + x(x + 4y + -2) * dy = 0 (1dx + dx2y) + x(x + 4y + -2) * dy = 0 Reorder the terms: 1dx + dx2y + x(-2 + x + 4y) * dy = 0 Reorder the terms for easier multiplication: 1dx + dx2y + x * dy(-2 + x + 4y) = 0 Multiply x * dy 1dx + dx2y + dxy(-2 + x + 4y) = 0 1dx + dx2y + (-2 * dxy + x * dxy + 4y * dxy) = 0 Reorder the terms: 1dx + dx2y + (-2dxy + 4dxy2 + dx2y) = 0 1dx + dx2y + (-2dxy + 4dxy2 + dx2y) = 0 Reorder the terms: 1dx + -2dxy + 4dxy2 + dx2y + dx2y = 0 Combine like terms: dx2y + dx2y = 2dx2y 1dx + -2dxy + 4dxy2 + 2dx2y = 0 Solving 1dx + -2dxy + 4dxy2 + 2dx2y = 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(1 + -2y + 4y2 + 2xy) = 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 + -2y + 4y2 + 2xy)' equal to zero and attempt to solve: Simplifying 1 + -2y + 4y2 + 2xy = 0 Reorder the terms: 1 + 2xy + -2y + 4y2 = 0 Solving 1 + 2xy + -2y + 4y2 = 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 + -2y + -1 + 4y2 = 0 + -1 Reorder the terms: 1 + -1 + 2xy + -2y + 4y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2xy + -2y + 4y2 = 0 + -1 2xy + -2y + 4y2 = 0 + -1 Combine like terms: 0 + -1 = -1 2xy + -2y + 4y2 = -1 Add '-2xy' to each side of the equation. 2xy + -2y + -2xy + 4y2 = -1 + -2xy Reorder the terms: 2xy + -2xy + -2y + 4y2 = -1 + -2xy Combine like terms: 2xy + -2xy = 0 0 + -2y + 4y2 = -1 + -2xy -2y + 4y2 = -1 + -2xy Add '2y' to each side of the equation. -2y + 2y + 4y2 = -1 + -2xy + 2y Combine like terms: -2y + 2y = 0 0 + 4y2 = -1 + -2xy + 2y 4y2 = -1 + -2xy + 2y Add '-4y2' to each side of the equation. 4y2 + -4y2 = -1 + -2xy + 2y + -4y2 Combine like terms: 4y2 + -4y2 = 0 0 = -1 + -2xy + 2y + -4y2 Simplifying 0 = -1 + -2xy + 2y + -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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