Maximum possible integer square root polynomial 1: easier (but still hard)

Find the maximum possible integral value of


Where x is an integer.


I will post a solution to this with a neat generalized formula 16 hours after this post if no one else has.

You may use a calculator

You may use all and any means possible of solving this problem, whether be it wolfram alpha, Python coding, or Java. Although I encourage you to use only a pencil and a hand held calculator because that is how I did it.

the harder version of this is here


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