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