SOLUTION: A colonel, on attempting to draw up his regiment in the form of a solid square, finds that he has 30 men left over, and that he would require 25 soliders in his regiment to increas

Question 221446: A colonel, on attempting to draw up his regiment in the form of a solid square, finds that he has 30 men left over, and that he would require 25 soliders in his regiment to increase the side of the square by one soldier. How many soldiers are there in the regiment?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A colonel, on attempting to draw up his regiment in the form of a solid square,
finds that he has 30 men left over, and that he would require 25 solders in his
regiment to increase the side of the square by one soldier.
How many soldiers are there in the regiment?
;
Let (x^2 + 30) = no. of soldiers in the regiment
:
It says that 25 more would give him one more in each side:
We can write that
(x + 1)^2 = x^2 + 30 + 25
:
x^2 + 2x + 1 = x^2 + 55
;
x^2 - x^2 + 2x = 55 - 1
:
2x = 54
x =
x = 27
therefore
27^2 + 30 = 759 soldiers
:
Is this true?
28^2 - 759 = 25
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