## BloomLocke367 one year ago Solve algebraically and confirm graphically. $$(x+11)^2=121$$

1. BloomLocke367

I got it down to $$x^2+22x=0$$

2. BloomLocke367

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

3. jdoe0001

I gather so....yes

4. jdoe0001

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

5. BloomLocke367

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

6. BloomLocke367

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.

7. mathstudent55

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

8. jdoe0001

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

9. BloomLocke367

$$x^2+22x+121$$. That's it expanded

10. BloomLocke367

but it is set equal to 121

11. mathstudent55

$$(x+11)^2=121$$ $$x^2 + 22x + 121 = 121$$ $$x^2 + 22x = 0$$ $$x(x + 22) = 0$$ Now continue.

12. geerky42

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

13. BloomLocke367

ohhhhhhhhhhhhhhhhh

14. jdoe0001

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

15. BloomLocke367

so x=0 and x=-22

16. mathstudent55

Correct.

17. BloomLocke367

Thank you for making me remember stuff that I forgot XD

18. BloomLocke367

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

19. jdoe0001

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

20. mathstudent55

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 $$x = -11$$

21. jim_thompson5910

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

22. mathstudent55

Now you need to do it graphically.

23. BloomLocke367

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.

24. BloomLocke367

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