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Simplifying (2x2y + -2x3) * dy + (4x3 + -6x2y + 2xy2) * dx = 0 Reorder the terms for easier multiplication: dy(2x2y + -2x3) + (4x3 + -6x2y + 2xy2) * dx = 0 (2x2y * dy + -2x3 * dy) + (4x3 + -6x2y + 2xy2) * dx = 0 (2dx2y2 + -2dx3y) + (4x3 + -6x2y + 2xy2) * dx = 0 Reorder the terms: 2dx2y2 + -2dx3y + (2xy2 + -6x2y + 4x3) * dx = 0 Reorder the terms for easier multiplication: 2dx2y2 + -2dx3y + dx(2xy2 + -6x2y + 4x3) = 0 2dx2y2 + -2dx3y + (2xy2 * dx + -6x2y * dx + 4x3 * dx) = 0 2dx2y2 + -2dx3y + (2dx2y2 + -6dx3y + 4dx4) = 0 Reorder the terms: 2dx2y2 + 2dx2y2 + -2dx3y + -6dx3y + 4dx4 = 0 Combine like terms: 2dx2y2 + 2dx2y2 = 4dx2y2 4dx2y2 + -2dx3y + -6dx3y + 4dx4 = 0 Combine like terms: -2dx3y + -6dx3y = -8dx3y 4dx2y2 + -8dx3y + 4dx4 = 0 Solving 4dx2y2 + -8dx3y + 4dx4 = 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), '4dx2'. 4dx2(y2 + -2xy + x2) = 0 Factor a trinomial. 4dx2((y + -1x)(y + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'dx2' equal to zero and attempt to solve: Simplifying dx2 = 0 Solving dx2 = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx2 = 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 '(y + -1x)' equal to zero and attempt to solve: Simplifying y + -1x = 0 Reorder the terms: -1x + y = 0 Solving -1x + y = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + x + y = 0 + x Combine like terms: -1x + x = 0 0 + y = 0 + x y = 0 + x Remove the zero: y = x Add '-1y' to each side of the equation. y + -1y = x + -1y Combine like terms: y + -1y = 0 0 = x + -1y Simplifying 0 = x + -1y 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 '(y + -1x)' equal to zero and attempt to solve: Simplifying y + -1x = 0 Reorder the terms: -1x + y = 0 Solving -1x + y = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + x + y = 0 + x Combine like terms: -1x + x = 0 0 + y = 0 + x y = 0 + x Remove the zero: y = x Add '-1y' to each side of the equation. y + -1y = x + -1y Combine like terms: y + -1y = 0 0 = x + -1y Simplifying 0 = x + -1y 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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