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Simplifying F(x) = 4lnx + -2x2 Multiply F * x xF = 4lnx + -2x2 Solving xF = 4lnx + -2x2 Solving for variable 'x'. Reorder the terms: -4lnx + xF + 2x2 = 4lnx + -2x2 + -4lnx + 2x2 Reorder the terms: -4lnx + xF + 2x2 = 4lnx + -4lnx + -2x2 + 2x2 Combine like terms: 4lnx + -4lnx = 0 -4lnx + xF + 2x2 = 0 + -2x2 + 2x2 -4lnx + xF + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -4lnx + xF + 2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-4ln + F + 2x) = 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 '(-4ln + F + 2x)' equal to zero and attempt to solve: Simplifying -4ln + F + 2x = 0 Reorder the terms: F + -4ln + 2x = 0 Solving F + -4ln + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1F' to each side of the equation. F + -4ln + -1F + 2x = 0 + -1F Reorder the terms: F + -1F + -4ln + 2x = 0 + -1F Combine like terms: F + -1F = 0 0 + -4ln + 2x = 0 + -1F -4ln + 2x = 0 + -1F Remove the zero: -4ln + 2x = -1F Add '4ln' to each side of the equation. -4ln + 4ln + 2x = -1F + 4ln Combine like terms: -4ln + 4ln = 0 0 + 2x = -1F + 4ln 2x = -1F + 4ln Divide each side by '2'. x = -0.5F + 2ln Simplifying x = -0.5F + 2lnSolution
x = {0, -0.5F + 2ln}
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