SOLUTION: Completing the square p squared+16p-22

Question 442268: Completing the square p squared+16p-22
Answer by ilana(307) (Show Source): You can put this solution on YOUR website!
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
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