How do I find the value of a and the value of b in this equation?

Question

The question is...

x²+4x-9=(x+a)²+b

Solve for a and for b.

I tried to figure this out, went crazy with my working over two A4 pages and came to no actual integer answer. I don’t know how to complete this, any assistance would be greatly appreciated :).

I’ve got exams coming up in 2 days so any assistance ASAP would be AMAZING :)

Answer 1

x^2 + 4x + 9 = (x+a)^2 + b

complete the square on the left side, take half of 4 and square it. (4/2)^2 = 4

add and subtract 4

(x^2+4x +4) +9-4 = (x+a)^2 + b

(x+4)^2 + 5 = (x+a)^2 + b

a =4, b = 5