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