For the equation 4x2+4kx+(k2−5)=0, where k is a real parameter:
a. (i) Rewrite the left-hand side as the sum of a perfect square in x and a constant that depends on k.
b. (ii) Using the form obtained in part (i), determine all real values of k for which the equation has equal real roots.
c. (iii) For k=3, solve the equation completely and state the nature of its roots.