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Simplifying 2x(y2 + 5x2) * dy + (y3 + -1x2y) * dx = 0 Reorder the terms: 2x(5x2 + y2) * dy + (y3 + -1x2y) * dx = 0 Reorder the terms for easier multiplication: 2x * dy(5x2 + y2) + (y3 + -1x2y) * dx = 0 Multiply x * dy 2dxy(5x2 + y2) + (y3 + -1x2y) * dx = 0 (5x2 * 2dxy + y2 * 2dxy) + (y3 + -1x2y) * dx = 0 Reorder the terms: (2dxy3 + 10dx3y) + (y3 + -1x2y) * dx = 0 (2dxy3 + 10dx3y) + (y3 + -1x2y) * dx = 0 Reorder the terms: 2dxy3 + 10dx3y + (-1x2y + y3) * dx = 0 Reorder the terms for easier multiplication: 2dxy3 + 10dx3y + dx(-1x2y + y3) = 0 2dxy3 + 10dx3y + (-1x2y * dx + y3 * dx) = 0 Reorder the terms: 2dxy3 + 10dx3y + (dxy3 + -1dx3y) = 0 2dxy3 + 10dx3y + (dxy3 + -1dx3y) = 0 Reorder the terms: 2dxy3 + dxy3 + 10dx3y + -1dx3y = 0 Combine like terms: 2dxy3 + dxy3 = 3dxy3 3dxy3 + 10dx3y + -1dx3y = 0 Combine like terms: 10dx3y + -1dx3y = 9dx3y 3dxy3 + 9dx3y = 0 Solving 3dxy3 + 9dx3y = 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), '3dxy'. 3dxy(y2 + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'dxy' equal to zero and attempt to solve: Simplifying dxy = 0 Solving dxy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dxy = 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 '(y2 + 3x2)' equal to zero and attempt to solve: Simplifying y2 + 3x2 = 0 Reorder the terms: 3x2 + y2 = 0 Solving 3x2 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-3x2' to each side of the equation. 3x2 + -3x2 + y2 = 0 + -3x2 Combine like terms: 3x2 + -3x2 = 0 0 + y2 = 0 + -3x2 y2 = 0 + -3x2 Remove the zero: y2 = -3x2 Add '-1y2' to each side of the equation. y2 + -1y2 = -3x2 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -3x2 + -1y2 Simplifying 0 = -3x2 + -1y2 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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