-xln(x)+x=0.5

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Solution for -xln(x)+x=0.5 equation: 


Simplifying
-1xln(x) + x = 0.5

Multiply lnx * x
-1lnx2 + x = 0.5

Solving
-1lnx2 + x = 0.5

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Add '-1x' to each side of the equation.
-1lnx2 + x + -1x = 0.5 + -1x

Combine like terms: x + -1x = 0
-1lnx2 + 0 = 0.5 + -1x
-1lnx2 = 0.5 + -1x

Divide each side by '-1nx2'.
l = -0.5n-1x-2 + n-1x-1

Simplifying
l = -0.5n-1x-2 + n-1x-1

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