Question

Complete the square on the following quadratic

x^2+22x+9=0
what value is added to both sides of the equation.

Answer 1

I don't understand this question. Did you do something to it when you posted it or is that the way it was presented to you? What exactly are you trying to do with that?

Answer 2

The original problem is x^2 + 22x + 9 = 0?

Answer 3

Yes

Answer 4

Do you know how to complete the square?

Answer 5

I use too

Answer 6

Ok, there are steps you follow every time to complete the square. I'll type them here and then we can do the problem...

Answer 7

Separate the x terms from the other ones with the equal sign.
Make sure the coefficient on the x^2 term is 1.
Take half the x term, square it, and add it to both sides.

Let's do those first.

Answer 8

\[x ^{2}+2x+9=0\]
The first step is to make sure the coefficient on the x^2 is 1 and it is, so we can move on.

Answer 9

Separate the x terms from everything else by moving everything else to the other side of the equals sign.
\[x ^{2}+22x=-9\]

Answer 10

What is the coefficient on the x term?

Answer 11

-9?

Answer 12

The coefficient on the x term is 22. See up above? 22x

Answer 13

Sorry I was gone for a minute...

Answer 14

We need to take half the value of that x term; take half the value of 22 and what do we have? What is half of 22?

Answer 15

11

Answer 16

Ok, next step is to square that number. What is 11 times 11?

Answer 17

121

Answer 18

Yes! THAT is the number you add to both sides of the equation. This is what you have then:
\[x ^{2}+22x+121=-9+121\]

Answer 19

That is the critical point where you just completed the square, because what you have done on the left side is created a perfect square trinomial that can be factored into this:
\[(x+11)^{2}\]

Answer 20

How far do you need to go with this? Do you have to solve it for x or what?

Answer 21

Just what is added to both side

Answer 22

ok then!

Answer 23

I Like when you help me

Answer 24

Thank you! That means a lot!

Answer 25

Your Welcome :)