Problem

(a) Express $9x^2-36x+8$ in the form $p(x+q)^2+r$, where $p$, $q$ and $r$ are constants.

(b) Hence find the set of values of the constant $k$ for which the equation $9x^2-36x+8=k$ has no real roots.

(c) Find the exact roots of the equation $9x^2-36x+8=-15$.