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Simplifying F(x) = (x3) + -6lnx Multiply F * x xF = (x3) + -6lnx xF = x3 + -6lnx Reorder the terms: xF = -6lnx + x3 Solving xF = -6lnx + x3 Solving for variable 'x'. Reorder the terms: 6lnx + xF + -1x3 = -6lnx + x3 + 6lnx + -1x3 Reorder the terms: 6lnx + xF + -1x3 = -6lnx + 6lnx + x3 + -1x3 Combine like terms: -6lnx + 6lnx = 0 6lnx + xF + -1x3 = 0 + x3 + -1x3 6lnx + xF + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 6lnx + xF + -1x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(6ln + F + -1x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(6ln + F + -1x2)' equal to zero and attempt to solve: Simplifying 6ln + F + -1x2 = 0 Reorder the terms: F + 6ln + -1x2 = 0 Solving F + 6ln + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1F' to each side of the equation. F + 6ln + -1F + -1x2 = 0 + -1F Reorder the terms: F + -1F + 6ln + -1x2 = 0 + -1F Combine like terms: F + -1F = 0 0 + 6ln + -1x2 = 0 + -1F 6ln + -1x2 = 0 + -1F Remove the zero: 6ln + -1x2 = -1F Add '-6ln' to each side of the equation. 6ln + -6ln + -1x2 = -1F + -6ln Combine like terms: 6ln + -6ln = 0 0 + -1x2 = -1F + -6ln -1x2 = -1F + -6ln Divide each side by '-1'. x2 = F + 6ln Simplifying x2 = F + 6ln The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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