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