SOLUTION: Homework problem: The formula N=4x^2+5x+1 represents the number of househoulds N, in thousands, in a certain city that has a computer x years after 1990. According to the formula,

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Question 113214: Homework problem: The formula N=4x^2+5x+1 represents the number of househoulds N, in thousands, in a certain city that has a computer x years after 1990. According to the formula, in what year were there 175 thousand households with computers in this city? I would like to see how this is worked out, not just get an answer. Thank you!
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
N=4x%5E2%2B5x%2B1 is the given function. We want to know x when N = 175. So,

4x%5E2%2B5x%2B1=175
4x%5E2%2B5x%2B1-175=0, subtract 175 from both sides
4x%5E2%2B5x-174=0, collect terms
As it happens, this trinomial is factorable:
4x%5E2%2B5x-174=%284x%2B29%29%28x-6%29, so
%284x%2B29%29%28x-6%29=0, and

x=6 or
x=-29%2F4
A negative number of years in this case would be absurd, so you can exclude the negative result. The answer is 6 years.

Hope this helps,
John