F(x)=x-(2lnx)

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Solution for F(x)=x-(2lnx) equation:


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) = 0

Subproblem 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 = 0

Subproblem 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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