$$x ^ { 2 } - 8 x - 29 \equiv ( x + a ) ^ { 2 } + b ,$$
where \(a\) and \(b\) are constants.
- Find the value of \(a\) and the value of \(b\).
- Hence, or otherwise, show that the roots of
$$x ^ { 2 } - 8 x - 29 = 0$$
are \(c \pm d \sqrt { } 5\), where \(c\) and \(d\) are integers to be found.