Question

Solve algebraically and confirm graphically.
\((x+11)^2=121\)

Answer 1

I got it down to \(x^2+22x=0\)

Answer 2

and I'm pretty sure I need to complete the square, right?

Answer 3

I gather so....yes

Answer 4

well... do you how to complete the square? :)

Answer 5

I did... lemme see if I can remember XD It's been almost an entire year since I've done it xp

Answer 6

and nope. I can't remember. Just tell me what to do first and I'm pretty sure I'll catch on quickly since I'm already somewhat familiar with it.

Answer 7

You don't need to complete the square.
Just factor out x on the left side.

Answer 8

hmmm actually. right.. as @mathstudent55 said... you could just do common factoring

Answer 9

\(x^2+22x+121\). That's it expanded

Answer 10

but it is set equal to 121

Answer 11

\((x+11)^2=121\)

\(x^2 + 22x + 121 = 121\)

\(x^2 + 22x = 0\)

\(x(x + 22) = 0\)

Now continue.

Answer 12

Factor x out, then use the fact that if ab=0, then a=0 OR b=0.

Answer 13

ohhhhhhhhhhhhhhhhh

Answer 14

\(x^2+22x=0\implies x(x+22)=0\implies
\begin{cases}
x=0\\
x+22=0
\end{cases}\)

Answer 15

so x=0 and x=-22

Answer 16

Correct.

Answer 17

Thank you for making me remember stuff that I forgot XD

Answer 18

But now I don't know who to medal >.<

Answer 19

well.. @BloomLocke367 that's non-important anyway :)

Answer 20

The way the problem was given originally, it was already a completed square.
You could have done this:

\((x + 11)^2 = 121\)

\(x + 11 = \pm \sqrt{121} \)

\(x + 11 = \pm 11\)

\(x + 11 = 11\) or \(x + 11 = -11\)

\(x = 0\) or \(x = -11\)

Answer 21

Why not just take the square root of both sides?
\[\large (x+11)^2 = 121\]
\[\large \sqrt{(x+11)^2} = \sqrt{121}\]
\[\large |x+11| = 11 \ ...\ \text{Rule:} \sqrt{x^2} = |x| \text{ where x is a real number}\]
\[\large x+11 = 11 \ \text{ or } \ x+11 = -11\]
\[\large x= ??\ \text{ or } \ x = ??\]

Answer 22

Now you need to do it graphically.

Answer 23

Wow, thank you for making me see things in many different ways. That helps a ton. Thank you all! I would give all of you a medal if I could.

Answer 24

oh my goodness these are getting more and more complex as they go on.