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Simplifying 3(x2 + y2 + x) * dx + (3xy) * dy = 0 Reorder the terms: 3(x + x2 + y2) * dx + (3xy) * dy = 0 Reorder the terms for easier multiplication: 3dx(x + x2 + y2) + (3xy) * dy = 0 (x * 3dx + x2 * 3dx + y2 * 3dx) + (3xy) * dy = 0 Reorder the terms: (3dxy2 + 3dx2 + 3dx3) + (3xy) * dy = 0 (3dxy2 + 3dx2 + 3dx3) + (3xy) * dy = 0 Remove parenthesis around (3xy) 3dxy2 + 3dx2 + 3dx3 + 3xy * dy = 0 Multiply xy * dy 3dxy2 + 3dx2 + 3dx3 + 3dxy2 = 0 Reorder the terms: 3dxy2 + 3dxy2 + 3dx2 + 3dx3 = 0 Combine like terms: 3dxy2 + 3dxy2 = 6dxy2 6dxy2 + 3dx2 + 3dx3 = 0 Solving 6dxy2 + 3dx2 + 3dx3 = 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), '3dx'. 3dx(2y2 + x + x2) = 0 Ignore the factor 3.Subproblem 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 '(2y2 + x + x2)' equal to zero and attempt to solve: Simplifying 2y2 + x + x2 = 0 Reorder the terms: x + x2 + 2y2 = 0 Solving x + x2 + 2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + x2 + -1x + 2y2 = 0 + -1x Reorder the terms: x + -1x + x2 + 2y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + x2 + 2y2 = 0 + -1x x2 + 2y2 = 0 + -1x Remove the zero: x2 + 2y2 = -1x Add '-1x2' to each side of the equation. x2 + -1x2 + 2y2 = -1x + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 2y2 = -1x + -1x2 2y2 = -1x + -1x2 Add '-2y2' to each side of the equation. 2y2 + -2y2 = -1x + -1x2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 0 = -1x + -1x2 + -2y2 Simplifying 0 = -1x + -1x2 + -2y2 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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