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Simplifying (x4 + 6x2 * y2 + y4) * dx + 4xy(x2 + y2) * dy = 0 Multiply x2 * y2 (x4 + 6x2y2 + y4) * dx + 4xy(x2 + y2) * dy = 0 Reorder the terms: (6x2y2 + x4 + y4) * dx + 4xy(x2 + y2) * dy = 0 Reorder the terms for easier multiplication: dx(6x2y2 + x4 + y4) + 4xy(x2 + y2) * dy = 0 (6x2y2 * dx + x4 * dx + y4 * dx) + 4xy(x2 + y2) * dy = 0 Reorder the terms: (dxy4 + 6dx3y2 + dx5) + 4xy(x2 + y2) * dy = 0 (dxy4 + 6dx3y2 + dx5) + 4xy(x2 + y2) * dy = 0 Reorder the terms for easier multiplication: dxy4 + 6dx3y2 + dx5 + 4xy * dy(x2 + y2) = 0 Multiply xy * dy dxy4 + 6dx3y2 + dx5 + 4dxy2(x2 + y2) = 0 dxy4 + 6dx3y2 + dx5 + (x2 * 4dxy2 + y2 * 4dxy2) = 0 Reorder the terms: dxy4 + 6dx3y2 + dx5 + (4dxy4 + 4dx3y2) = 0 dxy4 + 6dx3y2 + dx5 + (4dxy4 + 4dx3y2) = 0 Reorder the terms: dxy4 + 4dxy4 + 6dx3y2 + 4dx3y2 + dx5 = 0 Combine like terms: dxy4 + 4dxy4 = 5dxy4 5dxy4 + 6dx3y2 + 4dx3y2 + dx5 = 0 Combine like terms: 6dx3y2 + 4dx3y2 = 10dx3y2 5dxy4 + 10dx3y2 + dx5 = 0 Solving 5dxy4 + 10dx3y2 + dx5 = 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(5y4 + 10x2y2 + x4) = 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 '(5y4 + 10x2y2 + x4)' equal to zero and attempt to solve: Simplifying 5y4 + 10x2y2 + x4 = 0 Reorder the terms: 10x2y2 + x4 + 5y4 = 0 Solving 10x2y2 + x4 + 5y4 = 0 Move all terms containing d to the left, all other terms to the right. Add '-10x2y2' to each side of the equation. 10x2y2 + x4 + -10x2y2 + 5y4 = 0 + -10x2y2 Reorder the terms: 10x2y2 + -10x2y2 + x4 + 5y4 = 0 + -10x2y2 Combine like terms: 10x2y2 + -10x2y2 = 0 0 + x4 + 5y4 = 0 + -10x2y2 x4 + 5y4 = 0 + -10x2y2 Remove the zero: x4 + 5y4 = -10x2y2 Add '-1x4' to each side of the equation. x4 + -1x4 + 5y4 = -10x2y2 + -1x4 Combine like terms: x4 + -1x4 = 0 0 + 5y4 = -10x2y2 + -1x4 5y4 = -10x2y2 + -1x4 Add '-5y4' to each side of the equation. 5y4 + -5y4 = -10x2y2 + -1x4 + -5y4 Combine like terms: 5y4 + -5y4 = 0 0 = -10x2y2 + -1x4 + -5y4 Simplifying 0 = -10x2y2 + -1x4 + -5y4 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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