Quad Func Help

Stuck on some homework as the teacher was explaining it but not fully as there was about 10 minutes of the lesson left so it wasn't in depth teaching.
Just need some help or some steps on how to solve this question if anyone could help me
x^2-8x-29=(x+a)^2+b.
a) Find the value of A and the value of B
b) Hence, or otherwise, show that roots of-x^2-8x-29=0 are c+-droot5, where c and d are integers.

Stuck on some homework as the teacher was explaining it but not fully as there was about 10 minutes of the lesson left so it wasn't in depth teaching.
Just need some help or some steps on how to solve this question if anyone could help me
x^2-8x-29=(x+a)^2+b.
a) Find the value of A and the value of B
b) Hence, or otherwise, show that roots of-x^2-8x-29=0 are c+-droot5, where c and d are integers.

b) x^2-8x-29=0

use
If ax² + bx + c = 0 then x = .

compare answer with c+-d root 5

I got x^2-8x-29=x^2+2ax+a^2+b

so 2ax must be -8. so a is -4? and -4^2 is 16. but i need -29. so b=-49?
for part B, i got x = 4±3√5

You seem to have an idea so

$x^2-8x-29 = (x-4)^2-16-29 = (x-4)^2 - 45$

The next part is correct so I assume that you did mean 45 not 49

Stuck on some homework as the teacher was explaining it but not fully as there was about 10 minutes of the lesson left so it wasn't in depth teaching.
Just need some help or some steps on how to solve this question if anyone could help me
x^2-8x-29=(x+a)^2+b.
a) Find the value of A and the value of B
b) Hence, or otherwise, show that roots of-x^2-8x-29=0 are c+-droot5, where c and d are integers.