Quadratic word problem

Question

Translate to a quadratic equation, then solve using the quadratic formula.
The length of a rectangular air filter is 5 inches less than twice the width. Find the length and width of the filter if the area is 493 square inches.

Answer 1

w(2w - 5) = 493

2w² - 5w - 493 = 0

(2w + 29)(w - 34) = 0

 

2w + 29 = 0

2w = -29

w = -29/2

We don't measure in negatives!

 

w - 34 = 0

w = 34

 

l = 2(34) - 5 = 63