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Simplifying (3x2 + y2) * dx + (3x3 + -4xy) * dy = 0 Reorder the terms for easier multiplication: dx(3x2 + y2) + (3x3 + -4xy) * dy = 0 (3x2 * dx + y2 * dx) + (3x3 + -4xy) * dy = 0 Reorder the terms: (dxy2 + 3dx3) + (3x3 + -4xy) * dy = 0 (dxy2 + 3dx3) + (3x3 + -4xy) * dy = 0 Reorder the terms: dxy2 + 3dx3 + (-4xy + 3x3) * dy = 0 Reorder the terms for easier multiplication: dxy2 + 3dx3 + dy(-4xy + 3x3) = 0 dxy2 + 3dx3 + (-4xy * dy + 3x3 * dy) = 0 dxy2 + 3dx3 + (-4dxy2 + 3dx3y) = 0 Reorder the terms: dxy2 + -4dxy2 + 3dx3 + 3dx3y = 0 Combine like terms: dxy2 + -4dxy2 = -3dxy2 -3dxy2 + 3dx3 + 3dx3y = 0 Solving -3dxy2 + 3dx3 + 3dx3y = 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), '3dx'. 3dx(-1y2 + x2 + x2y) = 0 Ignore the factor 3.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 '(-1y2 + x2 + x2y)' equal to zero and attempt to solve: Simplifying -1y2 + x2 + x2y = 0 Reorder the terms: x2 + x2y + -1y2 = 0 Solving x2 + x2y + -1y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x2' to each side of the equation. x2 + x2y + -1x2 + -1y2 = 0 + -1x2 Reorder the terms: x2 + -1x2 + x2y + -1y2 = 0 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + x2y + -1y2 = 0 + -1x2 x2y + -1y2 = 0 + -1x2 Remove the zero: x2y + -1y2 = -1x2 Add '-1x2y' to each side of the equation. x2y + -1x2y + -1y2 = -1x2 + -1x2y Combine like terms: x2y + -1x2y = 0 0 + -1y2 = -1x2 + -1x2y -1y2 = -1x2 + -1x2y Add 'y2' to each side of the equation. -1y2 + y2 = -1x2 + -1x2y + y2 Combine like terms: -1y2 + y2 = 0 0 = -1x2 + -1x2y + y2 Simplifying 0 = -1x2 + -1x2y + y2 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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