Question

Complete the square to write c(x) = x2 - 16x + 84 in vertex form.

Answer 1

First step:
Rewrite your equation like this:
c(x) = (x2 - 16x + ____) + 84
Now we need to figure out what we want to be in that ____

Answer 2

b/2 quantity squared

Answer 3

ok.. lets wait for a response here.

Answer 4

wouldn't you put 16 in the blank?

Answer 5

and then add 16 to the other side?

Answer 6

no. like ehuman said you want (b/2)^2 in there. b = 16 in our example.
so take 16 / 2 and square the result. what do you get?

Answer 7

because 16/2 = 8
8 x 8 = 64!

Answer 8

yes. put a 64 in the ___. now, how do we compensate for adding that 64?

Answer 9

you add it to the opposite side? or do you add it to the 84?

Answer 10

subtract it. we are working on the same side of the equation...so to compensate for adding something, on the same side just subtract the same number.
c(x) = (x2 - 16x + 64) + 84 - 64

Answer 11

okay, so let me try and do the rest of the work and I will post it:)

Answer 12

alright. good luck

Answer 13

\[c(x) = (x^2 - 16x + 64) + 84 - 20\]
\[c(x) = (x^2 - 16x + 64) + 20\]
\[c(x) = (x - 8)(x - 8) + 20\]
\[c(x) = (x - 8)^2 + 20\]

?? @BangkokGarrett

Answer 14

the end there should be + 64
+ 84 - 20 is + 64