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Simplifying (2x2y + 2xy + 2x2) * dx + (2x3y + 2x2 + 2xy) * dy = 0 Reorder the terms: (2xy + 2x2 + 2x2y) * dx + (2x3y + 2x2 + 2xy) * dy = 0 Reorder the terms for easier multiplication: dx(2xy + 2x2 + 2x2y) + (2x3y + 2x2 + 2xy) * dy = 0 (2xy * dx + 2x2 * dx + 2x2y * dx) + (2x3y + 2x2 + 2xy) * dy = 0 (2dx2y + 2dx3 + 2dx3y) + (2x3y + 2x2 + 2xy) * dy = 0 Reorder the terms: 2dx2y + 2dx3 + 2dx3y + (2xy + 2x2 + 2x3y) * dy = 0 Reorder the terms for easier multiplication: 2dx2y + 2dx3 + 2dx3y + dy(2xy + 2x2 + 2x3y) = 0 2dx2y + 2dx3 + 2dx3y + (2xy * dy + 2x2 * dy + 2x3y * dy) = 0 2dx2y + 2dx3 + 2dx3y + (2dxy2 + 2dx2y + 2dx3y2) = 0 Reorder the terms: 2dxy2 + 2dx2y + 2dx2y + 2dx3 + 2dx3y + 2dx3y2 = 0 Combine like terms: 2dx2y + 2dx2y = 4dx2y 2dxy2 + 4dx2y + 2dx3 + 2dx3y + 2dx3y2 = 0 Solving 2dxy2 + 4dx2y + 2dx3 + 2dx3y + 2dx3y2 = 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), '2dx'. 2dx(y2 + 2xy + x2 + x2y + x2y2) = 0 Ignore the factor 2.Subproblem 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 '(y2 + 2xy + x2 + x2y + x2y2)' equal to zero and attempt to solve: Simplifying y2 + 2xy + x2 + x2y + x2y2 = 0 Reorder the terms: 2xy + x2 + x2y + x2y2 + y2 = 0 Solving 2xy + x2 + x2y + x2y2 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2xy' to each side of the equation. 2xy + x2 + x2y + x2y2 + -2xy + y2 = 0 + -2xy Reorder the terms: 2xy + -2xy + x2 + x2y + x2y2 + y2 = 0 + -2xy Combine like terms: 2xy + -2xy = 0 0 + x2 + x2y + x2y2 + y2 = 0 + -2xy x2 + x2y + x2y2 + y2 = 0 + -2xy Remove the zero: x2 + x2y + x2y2 + y2 = -2xy Add '-1x2' to each side of the equation. x2 + x2y + x2y2 + -1x2 + y2 = -2xy + -1x2 Reorder the terms: x2 + -1x2 + x2y + x2y2 + y2 = -2xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + x2y + x2y2 + y2 = -2xy + -1x2 x2y + x2y2 + y2 = -2xy + -1x2 Add '-1x2y' to each side of the equation. x2y + x2y2 + -1x2y + y2 = -2xy + -1x2 + -1x2y Reorder the terms: x2y + -1x2y + x2y2 + y2 = -2xy + -1x2 + -1x2y Combine like terms: x2y + -1x2y = 0 0 + x2y2 + y2 = -2xy + -1x2 + -1x2y x2y2 + y2 = -2xy + -1x2 + -1x2y Add '-1x2y2' to each side of the equation. x2y2 + -1x2y2 + y2 = -2xy + -1x2 + -1x2y + -1x2y2 Combine like terms: x2y2 + -1x2y2 = 0 0 + y2 = -2xy + -1x2 + -1x2y + -1x2y2 y2 = -2xy + -1x2 + -1x2y + -1x2y2 Add '-1y2' to each side of the equation. y2 + -1y2 = -2xy + -1x2 + -1x2y + -1x2y2 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -2xy + -1x2 + -1x2y + -1x2y2 + -1y2 Simplifying 0 = -2xy + -1x2 + -1x2y + -1x2y2 + -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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