- (a) Express \(4 x ^ { 2 } + 10 x - 24\) in the form \(a ( x + b ) ^ { 2 } + c\), where \(a , b , c\) are constants whose values are to be found.
(b) Hence evaluate the integral
$$\int _ { 3 } ^ { 5 } \frac { 6 } { \sqrt { 4 x ^ { 2 } + 10 x - 24 } } \mathrm {~d} x$$
Give your answer correct to 3 decimal places.