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Simplifying (4x + -2y + -9) * dx + -1(2x + -1y + 5) * dy = 0 Reorder the terms: (-9 + 4x + -2y) * dx + -1(2x + -1y + 5) * dy = 0 Reorder the terms for easier multiplication: dx(-9 + 4x + -2y) + -1(2x + -1y + 5) * dy = 0 (-9 * dx + 4x * dx + -2y * dx) + -1(2x + -1y + 5) * dy = 0 Reorder the terms: (-9dx + -2dxy + 4dx2) + -1(2x + -1y + 5) * dy = 0 (-9dx + -2dxy + 4dx2) + -1(2x + -1y + 5) * dy = 0 Reorder the terms: -9dx + -2dxy + 4dx2 + -1(5 + 2x + -1y) * dy = 0 Reorder the terms for easier multiplication: -9dx + -2dxy + 4dx2 + -1dy(5 + 2x + -1y) = 0 -9dx + -2dxy + 4dx2 + (5 * -1dy + 2x * -1dy + -1y * -1dy) = 0 Reorder the terms: -9dx + -2dxy + 4dx2 + (-2dxy + -5dy + 1dy2) = 0 -9dx + -2dxy + 4dx2 + (-2dxy + -5dy + 1dy2) = 0 Reorder the terms: -9dx + -2dxy + -2dxy + 4dx2 + -5dy + 1dy2 = 0 Combine like terms: -2dxy + -2dxy = -4dxy -9dx + -4dxy + 4dx2 + -5dy + 1dy2 = 0 Solving -9dx + -4dxy + 4dx2 + -5dy + 1dy2 = 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), 'd'. d(-9x + -4xy + 4x2 + -5y + y2) = 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 '(-9x + -4xy + 4x2 + -5y + y2)' equal to zero and attempt to solve: Simplifying -9x + -4xy + 4x2 + -5y + y2 = 0 Solving -9x + -4xy + 4x2 + -5y + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '9x' to each side of the equation. -9x + -4xy + 4x2 + -5y + 9x + y2 = 0 + 9x Reorder the terms: -9x + 9x + -4xy + 4x2 + -5y + y2 = 0 + 9x Combine like terms: -9x + 9x = 0 0 + -4xy + 4x2 + -5y + y2 = 0 + 9x -4xy + 4x2 + -5y + y2 = 0 + 9x Remove the zero: -4xy + 4x2 + -5y + y2 = 9x Add '4xy' to each side of the equation. -4xy + 4x2 + -5y + 4xy + y2 = 9x + 4xy Reorder the terms: -4xy + 4xy + 4x2 + -5y + y2 = 9x + 4xy Combine like terms: -4xy + 4xy = 0 0 + 4x2 + -5y + y2 = 9x + 4xy 4x2 + -5y + y2 = 9x + 4xy Add '-4x2' to each side of the equation. 4x2 + -5y + -4x2 + y2 = 9x + 4xy + -4x2 Reorder the terms: 4x2 + -4x2 + -5y + y2 = 9x + 4xy + -4x2 Combine like terms: 4x2 + -4x2 = 0 0 + -5y + y2 = 9x + 4xy + -4x2 -5y + y2 = 9x + 4xy + -4x2 Add '5y' to each side of the equation. -5y + 5y + y2 = 9x + 4xy + -4x2 + 5y Combine like terms: -5y + 5y = 0 0 + y2 = 9x + 4xy + -4x2 + 5y y2 = 9x + 4xy + -4x2 + 5y Add '-1y2' to each side of the equation. y2 + -1y2 = 9x + 4xy + -4x2 + 5y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = 9x + 4xy + -4x2 + 5y + -1y2 Simplifying 0 = 9x + 4xy + -4x2 + 5y + -1y2 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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