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x=1+(sin(x-(1/2)))/2 equation

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Numerical solution:

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The solution

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        sin(x - 1/2)
x = 1 + ------------
             2      
$$x = \frac{\sin{\left(x - \frac{1}{2} \right)}}{2} + 1$$
The graph
Numerical answer [src]
x1 = 1.38786221157087
x1 = 1.38786221157087