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bob012345

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- Is there an analytic solution to the simple equation ##x^{\alpha} +x =1## where ##\alpha## is a constant ?

Is there an analytic solution to the simple equation ##x^{\alpha} +x =1##? I can get to a solution by iteration or by graphical methods but I wish to find a closed form exact solution. ##\alpha## is a constant. I tried to put it into a form where I could use the quadratic formula but that didn't work i.e something like ##c^{2\beta} + c^{\beta} =1##. Thanks.