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Simplifying (x + 2y)(dx + -1dy) = (dx + dy) Multiply (x + 2y) * (dx + -1dy) (x(dx + -1dy) + 2y * (dx + -1dy)) = (dx + dy) ((dx * x + -1dy * x) + 2y * (dx + -1dy)) = (dx + dy) Reorder the terms: ((-1dxy + dx2) + 2y * (dx + -1dy)) = (dx + dy) ((-1dxy + dx2) + 2y * (dx + -1dy)) = (dx + dy) (-1dxy + dx2 + (dx * 2y + -1dy * 2y)) = (dx + dy) (-1dxy + dx2 + (2dxy + -2dy2)) = (dx + dy) Reorder the terms: (-1dxy + 2dxy + dx2 + -2dy2) = (dx + dy) Combine like terms: -1dxy + 2dxy = 1dxy (1dxy + dx2 + -2dy2) = (dx + dy) Remove parenthesis around (dx + dy) 1dxy + dx2 + -2dy2 = dx + dy Solving 1dxy + dx2 + -2dy2 = dx + dy Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1dx' to each side of the equation. 1dxy + dx2 + -1dx + -2dy2 = dx + -1dx + dy Reorder the terms: -1dx + 1dxy + dx2 + -2dy2 = dx + -1dx + dy Combine like terms: dx + -1dx = 0 -1dx + 1dxy + dx2 + -2dy2 = 0 + dy -1dx + 1dxy + dx2 + -2dy2 = dy Add '-1dy' to each side of the equation. -1dx + 1dxy + dx2 + -1dy + -2dy2 = dy + -1dy Combine like terms: dy + -1dy = 0 -1dx + 1dxy + dx2 + -1dy + -2dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-1x + xy + x2 + -1y + -2y2) = 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 '(-1x + xy + x2 + -1y + -2y2)' equal to zero and attempt to solve: Simplifying -1x + xy + x2 + -1y + -2y2 = 0 Solving -1x + xy + x2 + -1y + -2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + xy + x2 + -1y + x + -2y2 = 0 + x Reorder the terms: -1x + x + xy + x2 + -1y + -2y2 = 0 + x Combine like terms: -1x + x = 0 0 + xy + x2 + -1y + -2y2 = 0 + x xy + x2 + -1y + -2y2 = 0 + x Remove the zero: xy + x2 + -1y + -2y2 = x Add '-1xy' to each side of the equation. xy + x2 + -1y + -1xy + -2y2 = x + -1xy Reorder the terms: xy + -1xy + x2 + -1y + -2y2 = x + -1xy Combine like terms: xy + -1xy = 0 0 + x2 + -1y + -2y2 = x + -1xy x2 + -1y + -2y2 = x + -1xy Add '-1x2' to each side of the equation. x2 + -1y + -1x2 + -2y2 = x + -1xy + -1x2 Reorder the terms: x2 + -1x2 + -1y + -2y2 = x + -1xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + -1y + -2y2 = x + -1xy + -1x2 -1y + -2y2 = x + -1xy + -1x2 Add 'y' to each side of the equation. -1y + y + -2y2 = x + -1xy + -1x2 + y Combine like terms: -1y + y = 0 0 + -2y2 = x + -1xy + -1x2 + y -2y2 = x + -1xy + -1x2 + y Add '2y2' to each side of the equation. -2y2 + 2y2 = x + -1xy + -1x2 + y + 2y2 Combine like terms: -2y2 + 2y2 = 0 0 = x + -1xy + -1x2 + y + 2y2 Simplifying 0 = x + -1xy + -1x2 + y + 2y2 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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