Question 442268
If you add and subtract the same number, the expression's value doesn't change. That's why completing the square works.
So we want to make p^2 + 16p + _ a perfect square trinomial. That means p^2 + 16p + _ can be written (p + _)^2.
In general, (a + b)^2 = a^2 + 2ab + b^2.
In this case, a=p, so 2b=16. Therefore, b=8.
So b^2, the last term in the perfect square trinomial, is 64.
So the completed square expression is:
(p^2 + 16p + 64) - 22 - 64, or (p + 8)^2 - 86