afreemanny said:

q^2 - 16q + 14

GCF = 8

q^2 = (q)^2 = perfect square

64 = (8)^2 = perfect square

16q = 2(q)(8) middle term is twice the product of q and 8

a=q , b= 8

(q-8)^2

You didn't say what it was you were supposed to do. Completing the square? You're close.

GCF? I don't know what that has to do with completing the square.

16q = 2(q)(8) middle term is twice the product of q and 8

You have what you need in this statement. 8 is the magic number for this problem.

This won't do.

(q-8)^2 = q^2 - 16q + 64 <== That is NOT where you started.

All is not lost. You are close, again.

You have from the beginning q^2 - 16q + 14, but you can't make that 14 into a 64 just because you want to. You have to account for what you do. Getting from 14 to 64 requires 50.

q^2 - 16q + 14 + 50 - 50 <== This IS still what you started with. We added 50 that we needed, but subtracted it so we wouldn't change anything.

q^2 - 16q + 14 + 50 - 50 = q^2 - 16q + 64 - 50 = (q-8)^2 - 50

or, we may need this version

(q-8)^2 - 50 = (q-8)^2 - 2*(5^2)

Well, since you didn't provide an actual problem statement, you'll have to tell me if I guessed very well.