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Simplifying xdy + -1ydx = (x2 + xy + -2y2) * dx Combine like terms: dxy + -1dxy = 0 0 = (x2 + xy + -2y2) * dx Reorder the terms: 0 = (xy + x2 + -2y2) * dx Reorder the terms for easier multiplication: 0 = dx(xy + x2 + -2y2) 0 = (xy * dx + x2 * dx + -2y2 * dx) Reorder the terms: 0 = (-2dxy2 + dx2y + dx3) 0 = (-2dxy2 + dx2y + dx3) Solving 0 = -2dxy2 + dx2y + dx3 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2dxy2' to each side of the equation. 0 + 2dxy2 = -2dxy2 + dx2y + 2dxy2 + dx3 Remove the zero: 2dxy2 = -2dxy2 + dx2y + 2dxy2 + dx3 Reorder the terms: 2dxy2 = -2dxy2 + 2dxy2 + dx2y + dx3 Combine like terms: -2dxy2 + 2dxy2 = 0 2dxy2 = 0 + dx2y + dx3 2dxy2 = dx2y + dx3 Add '-1dx2y' to each side of the equation. 2dxy2 + -1dx2y = dx2y + -1dx2y + dx3 Combine like terms: dx2y + -1dx2y = 0 2dxy2 + -1dx2y = 0 + dx3 2dxy2 + -1dx2y = dx3 Add '-1dx3' to each side of the equation. 2dxy2 + -1dx2y + -1dx3 = dx3 + -1dx3 Combine like terms: dx3 + -1dx3 = 0 2dxy2 + -1dx2y + -1dx3 = 0 Factor out the Greatest Common Factor (GCF), 'dx'. dx(2y2 + -1xy + -1x2) = 0 Factor a trinomial. dx((y + -1x)(2y + x)) = 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 '(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 '(2y + x)' equal to zero and attempt to solve: Simplifying 2y + x = 0 Reorder the terms: x + 2y = 0 Solving x + 2y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + 2y = 0 + -1x Combine like terms: x + -1x = 0 0 + 2y = 0 + -1x 2y = 0 + -1x Remove the zero: 2y = -1x Add '-2y' to each side of the equation. 2y + -2y = -1x + -2y Combine like terms: 2y + -2y = 0 0 = -1x + -2y Simplifying 0 = -1x + -2y 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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