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Simplifying 8ydx + -1x(y2 + 12) * dy = 0 Reorder the terms: 8dxy + -1x(12 + y2) * dy = 0 Reorder the terms for easier multiplication: 8dxy + -1x * dy(12 + y2) = 0 Multiply x * dy 8dxy + -1dxy(12 + y2) = 0 8dxy + (12 * -1dxy + y2 * -1dxy) = 0 8dxy + (-12dxy + -1dxy3) = 0 Combine like terms: 8dxy + -12dxy = -4dxy -4dxy + -1dxy3 = 0 Solving -4dxy + -1dxy3 = 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), '-1dxy'. -1dxy(4 + y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor 'dxy' equal to zero and attempt to solve: Simplifying dxy = 0 Solving dxy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dxy = 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 '(4 + y2)' equal to zero and attempt to solve: Simplifying 4 + y2 = 0 Solving 4 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + y2 = 0 + -4 y2 = 0 + -4 Combine like terms: 0 + -4 = -4 y2 = -4 Add '-1y2' to each side of the equation. y2 + -1y2 = -4 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -4 + -1y2 Simplifying 0 = -4 + -1y2 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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