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Simplifying (y2 + 9) * dx + -5xy * dy = 0 Reorder the terms: (9 + y2) * dx + -5xy * dy = 0 Reorder the terms for easier multiplication: dx(9 + y2) + -5xy * dy = 0 (9 * dx + y2 * dx) + -5xy * dy = 0 (9dx + dxy2) + -5xy * dy = 0 Multiply xy * dy 9dx + dxy2 + -5dxy2 = 0 Combine like terms: dxy2 + -5dxy2 = -4dxy2 9dx + -4dxy2 = 0 Solving 9dx + -4dxy2 = 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(9 + -4y2) = 0 Factor a difference between two squares. dx((3 + 2y)(3 + -2y)) = 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 '(3 + 2y)' equal to zero and attempt to solve: Simplifying 3 + 2y = 0 Solving 3 + 2y = 0 Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2y = 0 + -3 2y = 0 + -3 Combine like terms: 0 + -3 = -3 2y = -3 Add '-2y' to each side of the equation. 2y + -2y = -3 + -2y Combine like terms: 2y + -2y = 0 0 = -3 + -2y Simplifying 0 = -3 + -2y 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 '(3 + -2y)' equal to zero and attempt to solve: Simplifying 3 + -2y = 0 Solving 3 + -2y = 0 Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2y = 0 + -3 -2y = 0 + -3 Combine like terms: 0 + -3 = -3 -2y = -3 Add '2y' to each side of the equation. -2y + 2y = -3 + 2y Combine like terms: -2y + 2y = 0 0 = -3 + 2y Simplifying 0 = -3 + 2y 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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