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Simplifying (x + y + -1) * dx + (x + ey) * dy = 0 Reorder the terms: (-1 + x + y) * dx + (x + ey) * dy = 0 Reorder the terms for easier multiplication: dx(-1 + x + y) + (x + ey) * dy = 0 (-1 * dx + x * dx + y * dx) + (x + ey) * dy = 0 Reorder the terms: (-1dx + dxy + dx2) + (x + ey) * dy = 0 (-1dx + dxy + dx2) + (x + ey) * dy = 0 Reorder the terms: -1dx + dxy + dx2 + (ey + x) * dy = 0 Reorder the terms for easier multiplication: -1dx + dxy + dx2 + dy(ey + x) = 0 -1dx + dxy + dx2 + (ey * dy + x * dy) = 0 -1dx + dxy + dx2 + (dey2 + dxy) = 0 Reorder the terms: dey2 + -1dx + dxy + dxy + dx2 = 0 Combine like terms: dxy + dxy = 2dxy dey2 + -1dx + 2dxy + dx2 = 0 Solving dey2 + -1dx + 2dxy + dx2 = 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(ey2 + -1x + 2xy + x2) = 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 '(ey2 + -1x + 2xy + x2)' equal to zero and attempt to solve: Simplifying ey2 + -1x + 2xy + x2 = 0 Solving ey2 + -1x + 2xy + x2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1ey2' to each side of the equation. ey2 + -1x + 2xy + -1ey2 + x2 = 0 + -1ey2 Reorder the terms: ey2 + -1ey2 + -1x + 2xy + x2 = 0 + -1ey2 Combine like terms: ey2 + -1ey2 = 0 0 + -1x + 2xy + x2 = 0 + -1ey2 -1x + 2xy + x2 = 0 + -1ey2 Remove the zero: -1x + 2xy + x2 = -1ey2 Add 'x' to each side of the equation. -1x + 2xy + x + x2 = -1ey2 + x Reorder the terms: -1x + x + 2xy + x2 = -1ey2 + x Combine like terms: -1x + x = 0 0 + 2xy + x2 = -1ey2 + x 2xy + x2 = -1ey2 + x Add '-2xy' to each side of the equation. 2xy + -2xy + x2 = -1ey2 + x + -2xy Combine like terms: 2xy + -2xy = 0 0 + x2 = -1ey2 + x + -2xy x2 = -1ey2 + x + -2xy Add '-1x2' to each side of the equation. x2 + -1x2 = -1ey2 + x + -2xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 = -1ey2 + x + -2xy + -1x2 Simplifying 0 = -1ey2 + x + -2xy + -1x2 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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