How to find the minima for $y = x^2 + a.x - \lfloor\sqrt{x^2+a.x - b}\rfloor^2$?

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Please guide in how to find the value of $x$ for which $y = x^2 + a.x - \lfloor\sqrt{x^2+a.x - b}\rfloor^2$ will be minimum.

I know this involves differentiation but am not sure on how to differentiate $\lfloor\sqrt{x^2+a.x - b}\rfloor^2$.