For N to end in 09, x must be of the form 50n±3 (50n±3)²=2500n²±300n+9 Notice the hundreds place digits are both odd. Since n² and n also have the same parity, the sum will always be even.
If you check (50n±13)² ends in 69 (50n±23)² ends in 29 (50n±33)² ends in 89 (50n±43)² ends in 49