Question

I need a refresher on completing the square:
x^2+14x+____

Answer 1

(half coefficient of x)^2....Add it to both sides

Answer 2

so x+14x+___=x?

Answer 3

Half the coefficient of x (keyword is coefficient. When you have half coefficient of x, square the total. We are referring to x of 14x. Not to be confused with the first term x^2

Answer 4

oh, yea, I did get that mixed up. ok (7)^2

Answer 5

which is 49

Answer 6

Yes

Answer 7

and thats the answer for the question on the reveiw. but what if I start out with three terms like x^2+16x-57?

Answer 8

I know I would move the 57 over to be =-57 and then I guess I'd do as we just did and half 16x (8)^2

Answer 9

Right. Careful with signs on 57.

Answer 10

oh yea, it changed to +57
ok, and now I have (x+8)^2= +/- sqrt121

Answer 11

oh wait, do I move the ^2 over the equal sign to do the sqrt? I don't think it can be both at the same time right?

Answer 12

it should be x+8=+/-sqrt11

Answer 13

I'm not sure what you are working on. Usually when you are doing complete square, you are trying to manipulate it in the form in order to answer some other question. You are not always trying to solve for x. So sometimes you leave it like this\[(x+8)^{2}=-7\]In this form you tackle stuff like questions regarding the circle or ellipses.

Answer 14

ok, that makes sense. I just wanted to make sure I could work the other kind as well. I think it will be the form for circles and ellipses on my test though

Answer 15

thanks @chaguanas