x^x-x!+x^2=248

The expression on the left-hand side of the equation is only defined when x is a Natural number, correct?

(You need to know that 0^0 is not defined and that x! is only defined for non-negative integers.)

Calculate a few values of the left-hand side; let x = 1, 2, 3, 4, 5.

See what happens.
 
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