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Simplifying (x + -2y + 9) * dx + -1(3x + -6y + 19) * dy = 0 Reorder the terms: (9 + x + -2y) * dx + -1(3x + -6y + 19) * dy = 0 Reorder the terms for easier multiplication: dx(9 + x + -2y) + -1(3x + -6y + 19) * dy = 0 (9 * dx + x * dx + -2y * dx) + -1(3x + -6y + 19) * dy = 0 Reorder the terms: (9dx + -2dxy + dx2) + -1(3x + -6y + 19) * dy = 0 (9dx + -2dxy + dx2) + -1(3x + -6y + 19) * dy = 0 Reorder the terms: 9dx + -2dxy + dx2 + -1(19 + 3x + -6y) * dy = 0 Reorder the terms for easier multiplication: 9dx + -2dxy + dx2 + -1dy(19 + 3x + -6y) = 0 9dx + -2dxy + dx2 + (19 * -1dy + 3x * -1dy + -6y * -1dy) = 0 Reorder the terms: 9dx + -2dxy + dx2 + (-3dxy + -19dy + 6dy2) = 0 9dx + -2dxy + dx2 + (-3dxy + -19dy + 6dy2) = 0 Reorder the terms: 9dx + -2dxy + -3dxy + dx2 + -19dy + 6dy2 = 0 Combine like terms: -2dxy + -3dxy = -5dxy 9dx + -5dxy + dx2 + -19dy + 6dy2 = 0 Solving 9dx + -5dxy + dx2 + -19dy + 6dy2 = 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 + -5xy + x2 + -19y + 6y2) = 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 + -5xy + x2 + -19y + 6y2)' equal to zero and attempt to solve: Simplifying 9x + -5xy + x2 + -19y + 6y2 = 0 Solving 9x + -5xy + x2 + -19y + 6y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-9x' to each side of the equation. 9x + -5xy + x2 + -19y + -9x + 6y2 = 0 + -9x Reorder the terms: 9x + -9x + -5xy + x2 + -19y + 6y2 = 0 + -9x Combine like terms: 9x + -9x = 0 0 + -5xy + x2 + -19y + 6y2 = 0 + -9x -5xy + x2 + -19y + 6y2 = 0 + -9x Remove the zero: -5xy + x2 + -19y + 6y2 = -9x Add '5xy' to each side of the equation. -5xy + x2 + -19y + 5xy + 6y2 = -9x + 5xy Reorder the terms: -5xy + 5xy + x2 + -19y + 6y2 = -9x + 5xy Combine like terms: -5xy + 5xy = 0 0 + x2 + -19y + 6y2 = -9x + 5xy x2 + -19y + 6y2 = -9x + 5xy Add '-1x2' to each side of the equation. x2 + -19y + -1x2 + 6y2 = -9x + 5xy + -1x2 Reorder the terms: x2 + -1x2 + -19y + 6y2 = -9x + 5xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + -19y + 6y2 = -9x + 5xy + -1x2 -19y + 6y2 = -9x + 5xy + -1x2 Add '19y' to each side of the equation. -19y + 19y + 6y2 = -9x + 5xy + -1x2 + 19y Combine like terms: -19y + 19y = 0 0 + 6y2 = -9x + 5xy + -1x2 + 19y 6y2 = -9x + 5xy + -1x2 + 19y Add '-6y2' to each side of the equation. 6y2 + -6y2 = -9x + 5xy + -1x2 + 19y + -6y2 Combine like terms: 6y2 + -6y2 = 0 0 = -9x + 5xy + -1x2 + 19y + -6y2 Simplifying 0 = -9x + 5xy + -1x2 + 19y + -6y2 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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