X^2 + 18x + c

Answer 1

To complete the square for the quadratic expression x^2 + 18x + c, we need to add and subtract (18/2)^2 = 81 to the expression:

x^2 + 18x + c + 81 - 81

Now, rearrange this expression:

x^2 + 18x + 81 - 81 + c

Factor the first three terms as a perfect square trinomial:

(x + 9)^2 + c - 81

So, x^2 + 18x + c can be rewritten as (x + 9)^2 + c - 81.