<PRE><B>Question 242509</B>
A general disposes his army into square battle formation. He finds he has 284 soldiers left over and above. But increasing each side of the square by one soldier he lacks 5 to fill up the new square. How many soldiers does the general have?
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Let the 1st square have x rows and x columns.
Equation: # of troops = x^2 + 284
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The 2nd square has x+1 rows and x+1 columns.
Equation: # of troops = (x+1)^2-5
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Equation:
# of troops = # of troops
x^2 + 284 = (x+1)^2-5
284 = 2x+1-5
2x = 288
x = 144
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# of troops = x^2 + 284
= 144^2+284
= 21020 
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Cheers,
Stan H.</PRE>