What is the complete range of values of $k$ for which the curves with equations $$y = x^3 - 12x$$ and $$y = k - (x-2)^2$$ intersect at three distinct points, of which exactly two have positive $x$-coordinates?
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What is the complete range of values of $k$ for which the curves with equations
$$y = x^3 - 12x$$
and
$$y = k - (x-2)^2$$
intersect at three distinct points, of which exactly two have positive $x$-coordinates?