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Simplifying (2y4 + -11x2y2 + -30x4) * dx + -1(3xy3) * dy = 0 Reorder the terms: (-11x2y2 + -30x4 + 2y4) * dx + -1(3xy3) * dy = 0 Reorder the terms for easier multiplication: dx(-11x2y2 + -30x4 + 2y4) + -1(3xy3) * dy = 0 (-11x2y2 * dx + -30x4 * dx + 2y4 * dx) + -1(3xy3) * dy = 0 Reorder the terms: (2dxy4 + -11dx3y2 + -30dx5) + -1(3xy3) * dy = 0 (2dxy4 + -11dx3y2 + -30dx5) + -1(3xy3) * dy = 0 Remove parenthesis around (3xy3) 2dxy4 + -11dx3y2 + -30dx5 + -1 * 3xy3 * dy = 0 Multiply -1 * 3 2dxy4 + -11dx3y2 + -30dx5 + -3xy3 * dy = 0 Multiply xy3 * dy 2dxy4 + -11dx3y2 + -30dx5 + -3dxy4 = 0 Reorder the terms: 2dxy4 + -3dxy4 + -11dx3y2 + -30dx5 = 0 Combine like terms: 2dxy4 + -3dxy4 = -1dxy4 -1dxy4 + -11dx3y2 + -30dx5 = 0 Solving -1dxy4 + -11dx3y2 + -30dx5 = 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), '-1dx'. -1dx(y4 + 11x2y2 + 30x4) = 0 Factor a trinomial. -1dx((y2 + 5x2)(y2 + 6x2)) = 0 Ignore the factor -1.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 + 5x2)' equal to zero and attempt to solve: Simplifying y2 + 5x2 = 0 Reorder the terms: 5x2 + y2 = 0 Solving 5x2 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-5x2' to each side of the equation. 5x2 + -5x2 + y2 = 0 + -5x2 Combine like terms: 5x2 + -5x2 = 0 0 + y2 = 0 + -5x2 y2 = 0 + -5x2 Remove the zero: y2 = -5x2 Add '-1y2' to each side of the equation. y2 + -1y2 = -5x2 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -5x2 + -1y2 Simplifying 0 = -5x2 + -1y2 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 '(y2 + 6x2)' equal to zero and attempt to solve: Simplifying y2 + 6x2 = 0 Reorder the terms: 6x2 + y2 = 0 Solving 6x2 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-6x2' to each side of the equation. 6x2 + -6x2 + y2 = 0 + -6x2 Combine like terms: 6x2 + -6x2 = 0 0 + y2 = 0 + -6x2 y2 = 0 + -6x2 Remove the zero: y2 = -6x2 Add '-1y2' to each side of the equation. y2 + -1y2 = -6x2 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -6x2 + -1y2 Simplifying 0 = -6x2 + -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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