I am trying to understand where I am getting these types of questions wrong, it seems algebra is not my best subject at the moment.

x^2 - 8x - 5

(x - 4)^2 - 16 + 5 = (x - 4)^2 - 11

Check it;

(x - 4)^2 - 11 = x^2 - 8x + 5 + 11 = x^2 - 8x + 16

I think the problem is in the (x - 4) area as this does not work back out to the original question. I have also tried (x - 2)^2 but this also results in x^2 + 4x + 4, which is not the same.

My course book talks a lot about halfing the coefficients of x, but I am missing something somewhere?