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Simplifying xy * dx + 2(x2 + 2y2) * dy = 0 Multiply xy * dx dx2y + 2(x2 + 2y2) * dy = 0 Reorder the terms for easier multiplication: dx2y + 2dy(x2 + 2y2) = 0 dx2y + (x2 * 2dy + 2y2 * 2dy) = 0 dx2y + (2dx2y + 4dy3) = 0 Combine like terms: dx2y + 2dx2y = 3dx2y 3dx2y + 4dy3 = 0 Solving 3dx2y + 4dy3 = 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), 'dy'. dy(3x2 + 4y2) = 0Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve: Simplifying dy = 0 Solving dy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy = 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 '(3x2 + 4y2)' equal to zero and attempt to solve: Simplifying 3x2 + 4y2 = 0 Solving 3x2 + 4y2 = 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 + 4y2 = 0 + -3x2 Combine like terms: 3x2 + -3x2 = 0 0 + 4y2 = 0 + -3x2 4y2 = 0 + -3x2 Remove the zero: 4y2 = -3x2 Add '-4y2' to each side of the equation. 4y2 + -4y2 = -3x2 + -4y2 Combine like terms: 4y2 + -4y2 = 0 0 = -3x2 + -4y2 Simplifying 0 = -3x2 + -4y2 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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