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Simplifying (9x + -4y + 4) * dx + -1(2x + -1y + 1) * dy = 0 Reorder the terms: (4 + 9x + -4y) * dx + -1(2x + -1y + 1) * dy = 0 Reorder the terms for easier multiplication: dx(4 + 9x + -4y) + -1(2x + -1y + 1) * dy = 0 (4 * dx + 9x * dx + -4y * dx) + -1(2x + -1y + 1) * dy = 0 Reorder the terms: (4dx + -4dxy + 9dx2) + -1(2x + -1y + 1) * dy = 0 (4dx + -4dxy + 9dx2) + -1(2x + -1y + 1) * dy = 0 Reorder the terms: 4dx + -4dxy + 9dx2 + -1(1 + 2x + -1y) * dy = 0 Reorder the terms for easier multiplication: 4dx + -4dxy + 9dx2 + -1dy(1 + 2x + -1y) = 0 4dx + -4dxy + 9dx2 + (1 * -1dy + 2x * -1dy + -1y * -1dy) = 0 Reorder the terms: 4dx + -4dxy + 9dx2 + (-2dxy + -1dy + 1dy2) = 0 4dx + -4dxy + 9dx2 + (-2dxy + -1dy + 1dy2) = 0 Reorder the terms: 4dx + -4dxy + -2dxy + 9dx2 + -1dy + 1dy2 = 0 Combine like terms: -4dxy + -2dxy = -6dxy 4dx + -6dxy + 9dx2 + -1dy + 1dy2 = 0 Solving 4dx + -6dxy + 9dx2 + -1dy + 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(4x + -6xy + 9x2 + -1y + 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 '(4x + -6xy + 9x2 + -1y + y2)' equal to zero and attempt to solve: Simplifying 4x + -6xy + 9x2 + -1y + y2 = 0 Solving 4x + -6xy + 9x2 + -1y + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-4x' to each side of the equation. 4x + -6xy + 9x2 + -1y + -4x + y2 = 0 + -4x Reorder the terms: 4x + -4x + -6xy + 9x2 + -1y + y2 = 0 + -4x Combine like terms: 4x + -4x = 0 0 + -6xy + 9x2 + -1y + y2 = 0 + -4x -6xy + 9x2 + -1y + y2 = 0 + -4x Remove the zero: -6xy + 9x2 + -1y + y2 = -4x Add '6xy' to each side of the equation. -6xy + 9x2 + -1y + 6xy + y2 = -4x + 6xy Reorder the terms: -6xy + 6xy + 9x2 + -1y + y2 = -4x + 6xy Combine like terms: -6xy + 6xy = 0 0 + 9x2 + -1y + y2 = -4x + 6xy 9x2 + -1y + y2 = -4x + 6xy Add '-9x2' to each side of the equation. 9x2 + -1y + -9x2 + y2 = -4x + 6xy + -9x2 Reorder the terms: 9x2 + -9x2 + -1y + y2 = -4x + 6xy + -9x2 Combine like terms: 9x2 + -9x2 = 0 0 + -1y + y2 = -4x + 6xy + -9x2 -1y + y2 = -4x + 6xy + -9x2 Add 'y' to each side of the equation. -1y + y + y2 = -4x + 6xy + -9x2 + y Combine like terms: -1y + y = 0 0 + y2 = -4x + 6xy + -9x2 + y y2 = -4x + 6xy + -9x2 + y Add '-1y2' to each side of the equation. y2 + -1y2 = -4x + 6xy + -9x2 + y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -4x + 6xy + -9x2 + y + -1y2 Simplifying 0 = -4x + 6xy + -9x2 + y + -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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