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Simplifying (x2 + 9) * dy = (2x + -10xy) * dx Reorder the terms: (9 + x2) * dy = (2x + -10xy) * dx Reorder the terms for easier multiplication: dy(9 + x2) = (2x + -10xy) * dx (9 * dy + x2 * dy) = (2x + -10xy) * dx Reorder the terms: (dx2y + 9dy) = (2x + -10xy) * dx (dx2y + 9dy) = (2x + -10xy) * dx Reorder the terms for easier multiplication: dx2y + 9dy = dx(2x + -10xy) dx2y + 9dy = (2x * dx + -10xy * dx) dx2y + 9dy = (2dx2 + -10dx2y) Solving dx2y + 9dy = 2dx2 + -10dx2y Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-2dx2' to each side of the equation. dx2y + -2dx2 + 9dy = 2dx2 + -2dx2 + -10dx2y Reorder the terms: -2dx2 + dx2y + 9dy = 2dx2 + -2dx2 + -10dx2y Combine like terms: 2dx2 + -2dx2 = 0 -2dx2 + dx2y + 9dy = 0 + -10dx2y -2dx2 + dx2y + 9dy = -10dx2y Add '10dx2y' to each side of the equation. -2dx2 + dx2y + 10dx2y + 9dy = -10dx2y + 10dx2y Combine like terms: dx2y + 10dx2y = 11dx2y -2dx2 + 11dx2y + 9dy = -10dx2y + 10dx2y Combine like terms: -10dx2y + 10dx2y = 0 -2dx2 + 11dx2y + 9dy = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-2x2 + 11x2y + 9y) = 0Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(-2x2 + 11x2y + 9y)' equal to zero and attempt to solve: Simplifying -2x2 + 11x2y + 9y = 0 Solving -2x2 + 11x2y + 9y = 0 Move all terms containing d to the left, all other terms to the right. Add '2x2' to each side of the equation. -2x2 + 11x2y + 2x2 + 9y = 0 + 2x2 Reorder the terms: -2x2 + 2x2 + 11x2y + 9y = 0 + 2x2 Combine like terms: -2x2 + 2x2 = 0 0 + 11x2y + 9y = 0 + 2x2 11x2y + 9y = 0 + 2x2 Remove the zero: 11x2y + 9y = 2x2 Add '-11x2y' to each side of the equation. 11x2y + -11x2y + 9y = 2x2 + -11x2y Combine like terms: 11x2y + -11x2y = 0 0 + 9y = 2x2 + -11x2y 9y = 2x2 + -11x2y Add '-9y' to each side of the equation. 9y + -9y = 2x2 + -11x2y + -9y Combine like terms: 9y + -9y = 0 0 = 2x2 + -11x2y + -9y Simplifying 0 = 2x2 + -11x2y + -9y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
d = {0}
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