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Simplifying y(x + 1) * dx + (x + 1) * dy = 0 Reorder the terms: y(1 + x) * dx + (x + 1) * dy = 0 Reorder the terms for easier multiplication: y * dx(1 + x) + (x + 1) * dy = 0 Multiply y * dx dxy(1 + x) + (x + 1) * dy = 0 (1 * dxy + x * dxy) + (x + 1) * dy = 0 (1dxy + dx2y) + (x + 1) * dy = 0 Reorder the terms: 1dxy + dx2y + (1 + x) * dy = 0 Reorder the terms for easier multiplication: 1dxy + dx2y + dy(1 + x) = 0 1dxy + dx2y + (1 * dy + x * dy) = 0 Reorder the terms: 1dxy + dx2y + (dxy + 1dy) = 0 1dxy + dx2y + (dxy + 1dy) = 0 Reorder the terms: 1dxy + dxy + dx2y + 1dy = 0 Combine like terms: 1dxy + dxy = 2dxy 2dxy + dx2y + 1dy = 0 Solving 2dxy + dx2y + 1dy = 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), 'dy'. dy(2x + x2 + 1) = 0 Factor a trinomial. dy((x + 1)(x + 1)) = 0Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve: Simplifying dy = 0 Solving dy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy = 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 '(x + 1)' equal to zero and attempt to solve: Simplifying x + 1 = 0 Reorder the terms: 1 + x = 0 Solving 1 + x = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -1x 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 + 1)' equal to zero and attempt to solve: Simplifying x + 1 = 0 Reorder the terms: 1 + x = 0 Solving 1 + x = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -1x 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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