SOLUTION: When the sum of a number plus 3 is squared, it is 13 more than the sum of the number plus 2 when squared.

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Question 202155: When the sum of a number plus 3 is squared, it is 13 more than the sum of the number plus 2 when squared.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let n = the required number, so...
%28n%2B3%29%5E2+=+%28n%2B2%29%5E2%2B13 Expand.
n%5E2%2B6n%2B9+=+n%5E2%2B4n%2B4%2B13 Subtract n%5E2 from both sides.
6n%2B9+=+4n%2B17 Subtract 4n from both sides.
2n%2B9+=+17 Subtract 9 from both sides.
2n+=+8 Finally, divide both sides by 2.
highlight%28n+=+4%29
Check:
%28n%2B3%29%5E2+=+%28n%2B2%29%5E2%2B13 Substitute n = 4.
%284%2B3%29%5E2+=+%284%2B2%29%5E2%2B13 Evaluate.
49+=+36%2B13
49+=+49 OK!