Explanation:
length = 8×width - 30
length × width = 3542
(8×width - 30)×width = 3542
8width² - 30width - 3542 = 0
4width² - 15width - 1771 = 0
the general solution to a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = width
a = 4
b = -15
c = -1771
width = (15 ± sqrt((-15)² - 4×4×-1771))/(2×4) =
= (15 ± sqrt(225 + 28336))/8 =
= (15 ± sqrt(28561))/8 = (15 ± 169)/8
width1 = (15 + 169)/8 = 184/8 = 23 ft
width2 = (15 - 169)/8 = -154/8 = -19.25 ft
a negative number for an actual length does not make any sense, so, only width = 23 ft is a valid solution.
length = 8×width - 30 = 8×23 - 30 = 184 - 30 = 154 ft