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Simplifying 2x(1 + y2) * dx + -1y(1 + 2x2) * dy = 0 Reorder the terms for easier multiplication: 2x * dx(1 + y2) + -1y(1 + 2x2) * dy = 0 Multiply x * dx 2dx2(1 + y2) + -1y(1 + 2x2) * dy = 0 (1 * 2dx2 + y2 * 2dx2) + -1y(1 + 2x2) * dy = 0 (2dx2 + 2dx2y2) + -1y(1 + 2x2) * dy = 0 Reorder the terms for easier multiplication: 2dx2 + 2dx2y2 + -1y * dy(1 + 2x2) = 0 Multiply y * dy 2dx2 + 2dx2y2 + -1dy2(1 + 2x2) = 0 2dx2 + 2dx2y2 + (1 * -1dy2 + 2x2 * -1dy2) = 0 Reorder the terms: 2dx2 + 2dx2y2 + (-2dx2y2 + -1dy2) = 0 2dx2 + 2dx2y2 + (-2dx2y2 + -1dy2) = 0 Combine like terms: 2dx2y2 + -2dx2y2 = 0 2dx2 + 0 + -1dy2 = 0 2dx2 + -1dy2 = 0 Solving 2dx2 + -1dy2 = 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), 'd'. d(2x2 + -1y2) = 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 '(2x2 + -1y2)' equal to zero and attempt to solve: Simplifying 2x2 + -1y2 = 0 Solving 2x2 + -1y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x2' to each side of the equation. 2x2 + -2x2 + -1y2 = 0 + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + -1y2 = 0 + -2x2 -1y2 = 0 + -2x2 Remove the zero: -1y2 = -2x2 Add 'y2' to each side of the equation. -1y2 + y2 = -2x2 + y2 Combine like terms: -1y2 + y2 = 0 0 = -2x2 + y2 Simplifying 0 = -2x2 + y2 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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