A large rectangular movie screen in an Imax Theater has an area of 9975 square feet. Find the dimensions of the screen if it is 10 feet longer than it is wide.

Answer 1

width ----- x ft
length = x+10 ft

x(x+10) = 9975
x^2 + 10x - 9975 = 0

intuition:
looks like the two roots are 10 apart
so I took √9975 = 99.87... or appr 100
guessed at 95 and 105, sure enough 95(105) = 9975 , so ....
(x+105)(x-95) = 0
since the width cannot be negative
x = 95

the screen is 95 ft by 105ft

of course we could have solved the equation just using the formula.