SOLUTION: 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

Question 242509: 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?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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
------------------------
Equation:
# of troops = # of troops
x^2 + 284 = (x+1)^2-5
284 = 2x+1-5
2x = 288
x = 144
--------------------
# of troops = x^2 + 284
= 144^2+284
= 21020
======================
Cheers,
Stan H.
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