don't understand the explanation in OG to this problem

Raj is right. If the units digit of a^2 is 9, only two numbers will square to give a units digit of 9: 3 or 7. See below.

Units digit when squaring:
0^2 = 0
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 6
5^2 = 5
6^2 = 6
7^2 = 9
8^2 = 4
9^2 = 1

So, a is either 3 or 7. If (a+1)^2 units digit is 4, then a must be 7, because (7+1)^2 = 8^2 = units digit of 4. a can't be 3, b/c (3+1)^2 = 4^2 = units digit of 6.

So if a is 7, then (a+2) = 9. 9^2 = units digit of 1.