The five observations 6, 8, 10, 12 and 14 have a population standard deviation of 22. When a sixth observation x is added to this set, the new standard deviation becomes 3.
(i) Form an equation in x using the information about the new standard deviation.
(ii) Solve the equation to obtain all possible values of x.
(iii) State the new mean of the six observations corresponding to each value of x found in part (ii).