Question

The square of a number decreased by the square of one half the number is 108. What is the number?

Answer 1

Let the number be n.  Then

n^2 - (n/2)^2 = 108.
                                          n
From this we get    n^2 - (---- )^2 = 108.
                                          2

 Mult. both terms by 4, with the result   4n^2 - n^2 = 432

Then 3n^2 = 432, and n^2 = 144.  n could be either 12 or -12.  You must check both answers by subst. them into the original equation.