(i) Write

\(8+7x-x^2\)

in the form \(a-(x-b)^2\), where \(a\) and \(b\) are constants.

(ii) Hence state the maximum value of \(8+7x-x^2\) and the value of \(x\) at which it occurs.

(iii) Using your answer to part (i), or otherwise, solve the equation

\(8+7z^2-z^4=0.\)