SOLUTION: The product of the page numbers on two consecutive pages of a boko is 600. Find the page numbers.

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Question 170547: The product of the page numbers on two consecutive pages of a boko is 600. Find the page numbers.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let n= the 1st page number
n+%2B+1 will be the next page number
given:
n%2A%28n%2B1%29+=+600
n%5E2+%2B+n+=+600
Complete the square by taking 1/2 of the co-efficient of x,
square it and add it to both sides.
n%5E2+%2B+n+%2B+1%2F4+=+600+%2B+1%2F4
Note that the left side is a perfect square
%28n+%2B+1%2F2%29%5E2+=+2401%2F4
Take the square root of both sides
n+%2B+1%2F2+=+49%2F2
n+=+49%2F2+-+1%2F2
n+=+24
n+%2B+1+=+25
check:
Does 24%2A25+=+600?
Yes
Note that I used only the (+) square root of 2401%2F4
since the (-) root is not useful