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Simplifying (8y + 10x) * dx + (5y + 7x) * dy = 0 Reorder the terms: (10x + 8y) * dx + (5y + 7x) * dy = 0 Reorder the terms for easier multiplication: dx(10x + 8y) + (5y + 7x) * dy = 0 (10x * dx + 8y * dx) + (5y + 7x) * dy = 0 Reorder the terms: (8dxy + 10dx2) + (5y + 7x) * dy = 0 (8dxy + 10dx2) + (5y + 7x) * dy = 0 Reorder the terms: 8dxy + 10dx2 + (7x + 5y) * dy = 0 Reorder the terms for easier multiplication: 8dxy + 10dx2 + dy(7x + 5y) = 0 8dxy + 10dx2 + (7x * dy + 5y * dy) = 0 8dxy + 10dx2 + (7dxy + 5dy2) = 0 Reorder the terms: 8dxy + 7dxy + 10dx2 + 5dy2 = 0 Combine like terms: 8dxy + 7dxy = 15dxy 15dxy + 10dx2 + 5dy2 = 0 Solving 15dxy + 10dx2 + 5dy2 = 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), '5d'. 5d(3xy + 2x2 + y2) = 0 Factor a trinomial. 5d((2x + y)(x + y)) = 0 Ignore the factor 5.Subproblem 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 '(2x + y)' equal to zero and attempt to solve: Simplifying 2x + y = 0 Solving 2x + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x' to each side of the equation. 2x + -2x + y = 0 + -2x Combine like terms: 2x + -2x = 0 0 + y = 0 + -2x y = 0 + -2x Remove the zero: y = -2x Add '-1y' to each side of the equation. y + -1y = -2x + -1y Combine like terms: y + -1y = 0 0 = -2x + -1y Simplifying 0 = -2x + -1y 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 '(x + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + y = 0 + -1x Combine like terms: x + -1x = 0 0 + y = 0 + -1x y = 0 + -1x Remove the zero: y = -1x Add '-1y' to each side of the equation. y + -1y = -1x + -1y Combine like terms: y + -1y = 0 0 = -1x + -1y Simplifying 0 = -1x + -1y 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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