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Simplifying F(x) = x + -1(2lnx) Multiply F * x xF = x + -1(2lnx) Remove parenthesis around (2lnx) xF = x + -1 * 2lnx Multiply -1 * 2 xF = x + -2lnx Reorder the terms: xF = -2lnx + x Solving xF = -2lnx + x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2lnx' to each side of the equation. 2lnx + xF = -2lnx + 2lnx + x Combine like terms: -2lnx + 2lnx = 0 2lnx + xF = 0 + x 2lnx + xF = x Add '-1x' to each side of the equation. 2lnx + -1x + xF = x + -1x Combine like terms: x + -1x = 0 2lnx + -1x + xF = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(2ln + -1 + F) = 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 '(2ln + -1 + F)' equal to zero and attempt to solve: Simplifying 2ln + -1 + F = 0 Reorder the terms: -1 + F + 2ln = 0 Solving -1 + F + 2ln = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + F + 1 + 2ln = 0 + 1 Reorder the terms: -1 + 1 + F + 2ln = 0 + 1 Combine like terms: -1 + 1 = 0 0 + F + 2ln = 0 + 1 F + 2ln = 0 + 1 Combine like terms: 0 + 1 = 1 F + 2ln = 1 Add '-1F' to each side of the equation. F + -1F + 2ln = 1 + -1F Combine like terms: F + -1F = 0 0 + 2ln = 1 + -1F 2ln = 1 + -1F Add '-2ln' to each side of the equation. 2ln + -2ln = 1 + -1F + -2ln Combine like terms: 2ln + -2ln = 0 0 = 1 + -1F + -2ln Simplifying 0 = 1 + -1F + -2ln 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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