x^2+8x complete the square to make the binomial a perfect trinomial

Answer 1

We have:

(a+b)^2 = a^2 + 2 a b + b^2

So, if we want the a^2 term is this identity to represent x^2, then the
2 a b term should be 8x. This means that b should be 4. Let's see what happens if we put a = x and b = 4:

(x+4)^2 = x^2 + 8 x + 16

So, we see that:

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