Constructing a Magic Square

please work on figuring out this 3X3 magic square, where each number from 1 to 9 is used once, and where all the rows, columns and diagonals add to 15!

 My solution:

1. The first thing I thought was to put 5 in the center because I found these pairs (1, 9), (2, 8), (3, 7), (4, 6) plus 5 is equal to 15.  

 2. 9 is the biggest number, start looking at this one. I can only find two combinations with 9 that sum to 15 : 1+5+9=15, 2+4+9=15. So 9 cannot be placed at corner. Then 1, 2 , and 4 can be placed in the square.

  3.  Then the rest of the numbers can be placed in the square by simply using addition.