SOLUTION: The following formula models the number of prison inmates, P, in thousands who are in US prisons x years after 1980. P=2x^2+20x+328 Find the first year in which the populatio

Algebra ->  Customizable Word Problem Solvers  -> Evaluation -> SOLUTION: The following formula models the number of prison inmates, P, in thousands who are in US prisons x years after 1980. P=2x^2+20x+328 Find the first year in which the populatio      Log On

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Question 672812: The following formula models the number of prison inmates, P, in thousands who are in US prisons x years after 1980.
P=2x^2+20x+328
Find the first year in which the population of US prisons was approximately 440,000 people.
Thank you for your help

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+P+ is in thousands, so
+440+=+2x%5E2+%2B+20x+%2B+328+
+2x%5E2+%2B+20x+-+112+=+0+
x%5E2+%2B+10x+-+56+=+0+
Complete the square
+x%5E2+%2B+10x+%2B+%2810%2F2%29%5E2+=+56+%2B+%2810%2F2%29%5E2+
+x%5E2+%2B+10x+%2B+25+=+56+%2B+25+
+%28+x+%2B+5+%29%5E2+=+81+
+x+%2B+5+=+9+
+x+=+4+
The year is 1984