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Simplifying (2y2 + -2y3) * dx + (4y3 + -6y2 * x + 2yx2) * dy = 0 Reorder the terms for easier multiplication: dx(2y2 + -2y3) + (4y3 + -6y2 * x + 2yx2) * dy = 0 (2y2 * dx + -2y3 * dx) + (4y3 + -6y2 * x + 2yx2) * dy = 0 (2dxy2 + -2dxy3) + (4y3 + -6y2 * x + 2yx2) * dy = 0 Multiply y2 * x 2dxy2 + -2dxy3 + (4y3 + -6xy2 + 2yx2) * dy = 0 Reorder the terms: 2dxy2 + -2dxy3 + (-6xy2 + 2x2y + 4y3) * dy = 0 Reorder the terms for easier multiplication: 2dxy2 + -2dxy3 + dy(-6xy2 + 2x2y + 4y3) = 0 2dxy2 + -2dxy3 + (-6xy2 * dy + 2x2y * dy + 4y3 * dy) = 0 2dxy2 + -2dxy3 + (-6dxy3 + 2dx2y2 + 4dy4) = 0 Combine like terms: -2dxy3 + -6dxy3 = -8dxy3 2dxy2 + -8dxy3 + 2dx2y2 + 4dy4 = 0 Solving 2dxy2 + -8dxy3 + 2dx2y2 + 4dy4 = 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), '2dy2'. 2dy2(x + -4xy + x2 + 2y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'dy2' equal to zero and attempt to solve: Simplifying dy2 = 0 Solving dy2 = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy2 = 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 '(x + -4xy + x2 + 2y2)' equal to zero and attempt to solve: Simplifying x + -4xy + x2 + 2y2 = 0 Solving x + -4xy + x2 + 2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -4xy + x2 + -1x + 2y2 = 0 + -1x Reorder the terms: x + -1x + -4xy + x2 + 2y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + -4xy + x2 + 2y2 = 0 + -1x -4xy + x2 + 2y2 = 0 + -1x Remove the zero: -4xy + x2 + 2y2 = -1x Add '4xy' to each side of the equation. -4xy + x2 + 4xy + 2y2 = -1x + 4xy Reorder the terms: -4xy + 4xy + x2 + 2y2 = -1x + 4xy Combine like terms: -4xy + 4xy = 0 0 + x2 + 2y2 = -1x + 4xy x2 + 2y2 = -1x + 4xy Add '-1x2' to each side of the equation. x2 + -1x2 + 2y2 = -1x + 4xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 2y2 = -1x + 4xy + -1x2 2y2 = -1x + 4xy + -1x2 Add '-2y2' to each side of the equation. 2y2 + -2y2 = -1x + 4xy + -1x2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 0 = -1x + 4xy + -1x2 + -2y2 Simplifying 0 = -1x + 4xy + -1x2 + -2y2 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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