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Simplifying (2x + -1y) * dx + -1(x + 4y) * dy = 0 Reorder the terms for easier multiplication: dx(2x + -1y) + -1(x + 4y) * dy = 0 (2x * dx + -1y * dx) + -1(x + 4y) * dy = 0 Reorder the terms: (-1dxy + 2dx2) + -1(x + 4y) * dy = 0 (-1dxy + 2dx2) + -1(x + 4y) * dy = 0 Reorder the terms for easier multiplication: -1dxy + 2dx2 + -1dy(x + 4y) = 0 -1dxy + 2dx2 + (x * -1dy + 4y * -1dy) = 0 -1dxy + 2dx2 + (-1dxy + -4dy2) = 0 Reorder the terms: -1dxy + -1dxy + 2dx2 + -4dy2 = 0 Combine like terms: -1dxy + -1dxy = -2dxy -2dxy + 2dx2 + -4dy2 = 0 Solving -2dxy + 2dx2 + -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), '2d'. 2d(-1xy + x2 + -2y2) = 0 Factor a trinomial. 2d((x + -2y)(x + y)) = 0 Ignore the factor 2.Subproblem 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 '(x + -2y)' equal to zero and attempt to solve: Simplifying x + -2y = 0 Solving x + -2y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + -2y = 0 + -1x Combine like terms: x + -1x = 0 0 + -2y = 0 + -1x -2y = 0 + -1x Remove the zero: -2y = -1x Add '2y' to each side of the equation. -2y + 2y = -1x + 2y Combine like terms: -2y + 2y = 0 0 = -1x + 2y Simplifying 0 = -1x + 2y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(x + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + y = 0 + -1x Combine like terms: x + -1x = 0 0 + y = 0 + -1x y = 0 + -1x Remove the zero: y = -1x Add '-1y' to each side of the equation. y + -1y = -1x + -1y Combine like terms: y + -1y = 0 0 = -1x + -1y Simplifying 0 = -1x + -1y 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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