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Simplifying (x2 + y2) * dx + -1(2xy * dy) = 0 Reorder the terms for easier multiplication: dx(x2 + y2) + -1(2xy * dy) = 0 (x2 * dx + y2 * dx) + -1(2xy * dy) = 0 Reorder the terms: (dxy2 + dx3) + -1(2xy * dy) = 0 (dxy2 + dx3) + -1(2xy * dy) = 0 Multiply xy * dy dxy2 + dx3 + -1(2dxy2) = 0 Remove parenthesis around (2dxy2) dxy2 + dx3 + -1 * 2dxy2 = 0 Multiply -1 * 2 dxy2 + dx3 + -2dxy2 = 0 Reorder the terms: dxy2 + -2dxy2 + dx3 = 0 Combine like terms: dxy2 + -2dxy2 = -1dxy2 -1dxy2 + dx3 = 0 Solving -1dxy2 + dx3 = 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), 'dx'. dx(-1y2 + x2) = 0 Factor a difference between two squares. dx((y + x)(-1y + x)) = 0Subproblem 1
Set the factor 'dx' equal to zero and attempt to solve: Simplifying dx = 0 Solving dx = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(y + x)' equal to zero and attempt to solve: Simplifying y + x = 0 Reorder the terms: 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.Subproblem 3
Set the factor '(-1y + x)' equal to zero and attempt to solve: Simplifying -1y + x = 0 Reorder the terms: x + -1y = 0 Solving x + -1y = 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 + -1y = 0 + -1x Combine like terms: x + -1x = 0 0 + -1y = 0 + -1x -1y = 0 + -1x Remove the zero: -1y = -1x Add 'y' to each side of the equation. -1y + y = -1x + y Combine like terms: -1y + y = 0 0 = -1x + y Simplifying 0 = -1x + y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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