The area of a rectangular swimming pool is 18x^2-9x-5. The length of the pool is 6x+5. What is the width of the pool?

1 Answer
Nghi N
Mar 7, 2018

(3x + 1)

Explanation:

Factor the trinomial f(x) by the new AC Method (Socratic Search):
#f(x) = 18x^2 - 9x - 5 =# 18(x + p)(x + q)
Converted trinomial:
#f'(x) = x^2 - 9x - 90 =# (x + p')(x + q')
Find p' and q' knowing the sum (-9) and the product (-90).
They are: p' = - 15 and q' = 6.
Back to f(x) --> #p = (p')/a = - 15/18 = - 5/6#, and #q = (q')/a = 6/18 = 1/3#.
Factored form
#f(x) = 18(x - 5/6)(x + 1/3) = (6x - 5)(3x + 1)#.
The pool 's width is (3x + 1)

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