Solving an equation by brute force within a range

[Gribouillis]

(x**0.5) isn't the same as square root, it gives another result, doesn't it?

When x is a nonnegative float, it should give the same result, but it turns out that for negative floats, Python returns the principal complex square root for x**0.5 while sqrt(x) raises a math domain error. So these are not exactly the same functions.

>>> (-1)**0.5
(6.123233995736766e-17+1j)
>>> from math import sqrt
>>> sqrt(-1)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: math domain error

For a general object, the expression x ** 0.5 returns x.__pow__(0.5), so the result depends on how the class of x defines the __pow__() method, which can be very arbitrary.