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Simplifying (x + 2x3) * dx + (y + 2y3) * dy = 0 Reorder the terms for easier multiplication: dx(x + 2x3) + (y + 2y3) * dy = 0 (x * dx + 2x3 * dx) + (y + 2y3) * dy = 0 (dx2 + 2dx4) + (y + 2y3) * dy = 0 Reorder the terms for easier multiplication: dx2 + 2dx4 + dy(y + 2y3) = 0 dx2 + 2dx4 + (y * dy + 2y3 * dy) = 0 dx2 + 2dx4 + (dy2 + 2dy4) = 0 Solving dx2 + 2dx4 + dy2 + 2dy4 = 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(x2 + 2x4 + y2 + 2y4) = 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 '(x2 + 2x4 + y2 + 2y4)' equal to zero and attempt to solve: Simplifying x2 + 2x4 + y2 + 2y4 = 0 Solving x2 + 2x4 + y2 + 2y4 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x2' to each side of the equation. x2 + 2x4 + y2 + -1x2 + 2y4 = 0 + -1x2 Reorder the terms: x2 + -1x2 + 2x4 + y2 + 2y4 = 0 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 2x4 + y2 + 2y4 = 0 + -1x2 2x4 + y2 + 2y4 = 0 + -1x2 Remove the zero: 2x4 + y2 + 2y4 = -1x2 Add '-2x4' to each side of the equation. 2x4 + y2 + -2x4 + 2y4 = -1x2 + -2x4 Reorder the terms: 2x4 + -2x4 + y2 + 2y4 = -1x2 + -2x4 Combine like terms: 2x4 + -2x4 = 0 0 + y2 + 2y4 = -1x2 + -2x4 y2 + 2y4 = -1x2 + -2x4 Add '-1y2' to each side of the equation. y2 + -1y2 + 2y4 = -1x2 + -2x4 + -1y2 Combine like terms: y2 + -1y2 = 0 0 + 2y4 = -1x2 + -2x4 + -1y2 2y4 = -1x2 + -2x4 + -1y2 Add '-2y4' to each side of the equation. 2y4 + -2y4 = -1x2 + -2x4 + -1y2 + -2y4 Combine like terms: 2y4 + -2y4 = 0 0 = -1x2 + -2x4 + -1y2 + -2y4 Simplifying 0 = -1x2 + -2x4 + -1y2 + -2y4 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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