1. You have:
2p²-15p+8=43
2p²-15p-35=0
2. the leading coefficient "a" must be 1. So, you need to divide the terms by 2:
p²-(15p/2)-(35/2)=0
3. Now, you have:
(b/2)²=(15/2/2)²=(15/4)²
p²-15p-(15/4)²=35+(15/4)²
(p-15/4)²=35+225/16
4. Finally, you obtain:
(p-15/4)²=505/16
