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