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Simplifying t * ln(s2t + 8t2) * ds + -1dt = 0 Reorder the terms for easier multiplication: t * ln * ds(s2t + 8t2) + -1dt = 0 Multiply t * ln lnt * ds(s2t + 8t2) + -1dt = 0 Multiply lnt * ds dlnst(s2t + 8t2) + -1dt = 0 (s2t * dlnst + 8t2 * dlnst) + -1dt = 0 Reorder the terms: (8dlnst3 + dlns3t2) + -1dt = 0 (8dlnst3 + dlns3t2) + -1dt = 0 Solving 8dlnst3 + dlns3t2 + -1dt = 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), 'dt'. dt(8lnst2 + lns3t + -1) = 0Subproblem 1
Set the factor 'dt' equal to zero and attempt to solve: Simplifying dt = 0 Solving dt = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dt = 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 '(8lnst2 + lns3t + -1)' equal to zero and attempt to solve: Simplifying 8lnst2 + lns3t + -1 = 0 Reorder the terms: -1 + 8lnst2 + lns3t = 0 Solving -1 + 8lnst2 + lns3t = 0 Move all terms containing d to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 8lnst2 + 1 + lns3t = 0 + 1 Reorder the terms: -1 + 1 + 8lnst2 + lns3t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 8lnst2 + lns3t = 0 + 1 8lnst2 + lns3t = 0 + 1 Combine like terms: 0 + 1 = 1 8lnst2 + lns3t = 1 Add '-8lnst2' to each side of the equation. 8lnst2 + -8lnst2 + lns3t = 1 + -8lnst2 Combine like terms: 8lnst2 + -8lnst2 = 0 0 + lns3t = 1 + -8lnst2 lns3t = 1 + -8lnst2 Add '-1lns3t' to each side of the equation. lns3t + -1lns3t = 1 + -8lnst2 + -1lns3t Combine like terms: lns3t + -1lns3t = 0 0 = 1 + -8lnst2 + -1lns3t Simplifying 0 = 1 + -8lnst2 + -1lns3t 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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