Consider the equation (x−4)2−5(x−4)−36=0.
a. (i) Let t=x−4. Re-express the given equation entirely in terms of t.
b. (ii) Solve the equation obtained in (i) for t.
c. (iii) Hence determine all corresponding values of x.
d. (iv) State, with reason, whether the roots of the original equation in x are real and distinct, real and equal, or non-real.