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Simplifying (x2) * dy = (4x2 + 7xy + 2y2) * dx Multiply x2 * dy dx2y = (4x2 + 7xy + 2y2) * dx Reorder the terms: dx2y = (7xy + 4x2 + 2y2) * dx Reorder the terms for easier multiplication: dx2y = dx(7xy + 4x2 + 2y2) dx2y = (7xy * dx + 4x2 * dx + 2y2 * dx) Reorder the terms: dx2y = (2dxy2 + 7dx2y + 4dx3) dx2y = (2dxy2 + 7dx2y + 4dx3) Solving dx2y = 2dxy2 + 7dx2y + 4dx3 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. -2dxy2 + dx2y = 2dxy2 + 7dx2y + -2dxy2 + 4dx3 Reorder the terms: -2dxy2 + dx2y = 2dxy2 + -2dxy2 + 7dx2y + 4dx3 Combine like terms: 2dxy2 + -2dxy2 = 0 -2dxy2 + dx2y = 0 + 7dx2y + 4dx3 -2dxy2 + dx2y = 7dx2y + 4dx3 Add '-7dx2y' to each side of the equation. -2dxy2 + dx2y + -7dx2y = 7dx2y + -7dx2y + 4dx3 Combine like terms: dx2y + -7dx2y = -6dx2y -2dxy2 + -6dx2y = 7dx2y + -7dx2y + 4dx3 Combine like terms: 7dx2y + -7dx2y = 0 -2dxy2 + -6dx2y = 0 + 4dx3 -2dxy2 + -6dx2y = 4dx3 Add '-4dx3' to each side of the equation. -2dxy2 + -6dx2y + -4dx3 = 4dx3 + -4dx3 Combine like terms: 4dx3 + -4dx3 = 0 -2dxy2 + -6dx2y + -4dx3 = 0 Factor out the Greatest Common Factor (GCF), '-2dx'. -2dx(y2 + 3xy + 2x2) = 0 Factor a trinomial. -2dx((y + x)(y + 2x)) = 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 '(y + x)' equal to zero and attempt to solve: Simplifying y + x = 0 Reorder the terms: x + y = 0 Solving x + y = 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 + y = 0 + -1x Combine like terms: x + -1x = 0 0 + y = 0 + -1x y = 0 + -1x Remove the zero: y = -1x Add '-1y' to each side of the equation. y + -1y = -1x + -1y Combine like terms: y + -1y = 0 0 = -1x + -1y Simplifying 0 = -1x + -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 + 2x)' equal to zero and attempt to solve: Simplifying y + 2x = 0 Reorder the terms: 2x + y = 0 Solving 2x + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x' to each side of the equation. 2x + -2x + y = 0 + -2x Combine like terms: 2x + -2x = 0 0 + y = 0 + -2x y = 0 + -2x Remove the zero: y = -2x Add '-1y' to each side of the equation. y + -1y = -2x + -1y Combine like terms: y + -1y = 0 0 = -2x + -1y Simplifying 0 = -2x + -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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