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