SOLUTION: The cost of a project is 14,850,000 the tax needed was calculated using census data, but a mistake showed that the population is actually 2200 people more which will reduce the tax

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Question 671630: The cost of a project is 14,850,000 the tax needed was calculated using census data, but a mistake showed that the population is actually 2200 people more which will reduce the tax needed per person by $75. What is the population?
I thought 14,850,000/(p+220) = 14,850,000/p - 75
and then tried to solve for p using LCD but it did not work out.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Looks like the right equation
+14850000+%2F+%28+p+%2B+2200+%29+=+14850000+%2F+p+-+75+
Multiply both sides by +p%2A%28+p+%2B+2200+%29+
+14850000p+=+14850000%2A%28+p+%2B+2200+%29+-+75p%2A%28+p+%2B+2200+%29+
+14850000p+=+14850000p+%2B+2200%2A14850000+-+75p%5E2+-+165000p+%29+
+75p%5E2+%2B+165000p+-+32670000000+=+0+
Divide through by +75+
+p%5E2+%2B+2200p+=+435600000+
Complete the square
+p%5E2+%2B+2200p+%2B+%28+2200%2F2+%29%5E2+=+435600000+%2B+%28+2200%2F2+%29%5E2+
+p%5E2+%2B+2200p+%2B+121000+=+435600000+%2B+121000+
+p%5E2+%2B+2200p+%2B+121000+=+435721000+
+%28+p+%2B+1100+%29%5E2+=+435721000+
+p+%2B+110+=+20873.9+
+p+=+20764+
--------------
check answer:
+14850000+%2F+%28+p+%2B+2200+%29+=+14850000+%2F+p+-+75+
+14850000+%2F+%28+20763.9+%2B+2200+%29+=+14850000+%2F+20763.9+-+75+
+14850000+%2F+22963.9+=+14850000+%2F+20763.9+-+75+
+646.66716+=+715.18356+-+75+
+646.66716+=+640.18356+
this is close, but I went off somewhere
maybe you can see it.