Solve x in Unsolvable Equation: d/(1-COS(L/(2*x)))

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The equation x = d/(1-COS(L/(2*x))) with L=28 and d=0.2 is challenging to solve algebraically. Initial attempts yielded an approximate value of x around 490 through trial and error. However, numerical methods are necessary for a more accurate solution. Using Maple, a more precise value of x is calculated to be approximately 1.0618829. This highlights the limitations of traditional calculators and the effectiveness of numerical techniques for such equations.
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Solve for x:

x=d/(1-COS(L/(2*x)))

where L=28 and d=0.2


I have been able to get x~490 by "guessing" values for x and computing, then repeating until both sides are equal.

There must be a better way, although neither my TI-89 nor Mathematica are able to do it.
 
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It's unsolvable by algebraic methods. The best you can do is to use numerical techniques to get approximate values.
 
When I solve this numerically with Maple I get x = 1.0618829.
 

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