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Simplifying Sqrt(3 + y2) * dx = (x2y + y) * dy Reorder the terms for easier multiplication: qrtS * dx(3 + y2) = (x2y + y) * dy Multiply qrtS * dx dqrtxS(3 + y2) = (x2y + y) * dy (3 * dqrtxS + y2 * dqrtxS) = (x2y + y) * dy (3dqrtxS + dqrtxy2S) = (x2y + y) * dy Reorder the terms for easier multiplication: 3dqrtxS + dqrtxy2S = dy(x2y + y) 3dqrtxS + dqrtxy2S = (x2y * dy + y * dy) 3dqrtxS + dqrtxy2S = (dx2y2 + dy2) Solving 3dqrtxS + dqrtxy2S = dx2y2 + dy2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1dx2y2' to each side of the equation. 3dqrtxS + dqrtxy2S + -1dx2y2 = dx2y2 + -1dx2y2 + dy2 Combine like terms: dx2y2 + -1dx2y2 = 0 3dqrtxS + dqrtxy2S + -1dx2y2 = 0 + dy2 3dqrtxS + dqrtxy2S + -1dx2y2 = dy2 Add '-1dy2' to each side of the equation. 3dqrtxS + dqrtxy2S + -1dx2y2 + -1dy2 = dy2 + -1dy2 Combine like terms: dy2 + -1dy2 = 0 3dqrtxS + dqrtxy2S + -1dx2y2 + -1dy2 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(3qrtxS + qrtxy2S + -1x2y2 + -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 '(3qrtxS + qrtxy2S + -1x2y2 + -1y2)' equal to zero and attempt to solve: Simplifying 3qrtxS + qrtxy2S + -1x2y2 + -1y2 = 0 Solving 3qrtxS + qrtxy2S + -1x2y2 + -1y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-3qrtxS' to each side of the equation. 3qrtxS + qrtxy2S + -1x2y2 + -3qrtxS + -1y2 = 0 + -3qrtxS Reorder the terms: 3qrtxS + -3qrtxS + qrtxy2S + -1x2y2 + -1y2 = 0 + -3qrtxS Combine like terms: 3qrtxS + -3qrtxS = 0 0 + qrtxy2S + -1x2y2 + -1y2 = 0 + -3qrtxS qrtxy2S + -1x2y2 + -1y2 = 0 + -3qrtxS Remove the zero: qrtxy2S + -1x2y2 + -1y2 = -3qrtxS Add '-1qrtxy2S' to each side of the equation. qrtxy2S + -1x2y2 + -1qrtxy2S + -1y2 = -3qrtxS + -1qrtxy2S Reorder the terms: qrtxy2S + -1qrtxy2S + -1x2y2 + -1y2 = -3qrtxS + -1qrtxy2S Combine like terms: qrtxy2S + -1qrtxy2S = 0 0 + -1x2y2 + -1y2 = -3qrtxS + -1qrtxy2S -1x2y2 + -1y2 = -3qrtxS + -1qrtxy2S Add 'x2y2' to each side of the equation. -1x2y2 + x2y2 + -1y2 = -3qrtxS + -1qrtxy2S + x2y2 Combine like terms: -1x2y2 + x2y2 = 0 0 + -1y2 = -3qrtxS + -1qrtxy2S + x2y2 -1y2 = -3qrtxS + -1qrtxy2S + x2y2 Add 'y2' to each side of the equation. -1y2 + y2 = -3qrtxS + -1qrtxy2S + x2y2 + y2 Combine like terms: -1y2 + y2 = 0 0 = -3qrtxS + -1qrtxy2S + x2y2 + y2 Simplifying 0 = -3qrtxS + -1qrtxy2S + x2y2 + 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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