SOLUTION: The difference between the square of a positive integer and the square of one half the number is 243. Find the number.

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Question 1053110: The difference between the square of a positive integer and the square of one half the number is 243. Find the number.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
number is x
x^2-(x/2)^2=243
x^2-(1/4)x^2=243
(3/4)x^2=243
x^2=243*4/3=324
x=sqrt(324)=18
the number is 18, its square is 324, and half of 18 squared is 81, which is 243 less than 324.