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How to do this question using completing the square.

The question is n^2 + 13n + 22 = 7

^ = power of...

¬ = square root

I got -6.5 = + or - ¬(-15). I'm guessing it's wrong though since you can't square root a negative number. So what's the real answer and your method of working it out would be appreciated. Thanks in advance!
Original post by Dr.Pwepper
The question is n^2 + 13n + 22 = 7

^ = power of...

¬ = square root

I got -6.5 = + or - ¬(-15). I'm guessing it's wrong though since you can't square root a negative number. So what's the real answer and your method of working it out would be appreciated. Thanks in advance!


n2 + 13n + 22 = 7

n2 + 13n + 15 = 0

(n + 13/2)2 - (13/2)2 + 15 = 0

(n + 13/2)2 - 169/4 + 15 = 0

(n + 13/2)2 - 169/4 + 60/4 = 0

(n + 13/2)2 - 100/4 = 0

(n + 13/2)2 - 25 = 0

(n + 13/2)2 = 25

n + 13/2 = root 25

n + 13/2 = +/- 5

n = -6.5 +/- 5

n = -1.5 or -11.5

:biggrin:
Reply 2
Avatar for msmith2512
msmith2512
1
-169/4 + 60/4 does not equal -100/4.

Replace with -109/4 which does not calculate as nicely.
[(n+6.5)2−42.25]+22=7[(n+6.5)^2-42.25]+22=7

(n+6.5)2=27.25(n+6.5)^2=27.25

n=±27.25−6.5n=\pm \sqrt{27.25}-6.5

Original post by thegodofgod
(n + 13/2)2 - 169/4 + 60/4 = 0

(n + 13/2)2 - 100/4 = 0


Note sure I agree with your calculation in this step...
Original post by Chwirkytheappleboy
[(n+6.5)2−42.25]+22=7[(n+6.5)^2-42.25]+22=7

(n+6.5)2=27.25(n+6.5)^2=27.25

n=±27.25−6.5n=\pm \sqrt{27.25}-6.5



Note sure I agree with your calculation in this step...


Woops - meant 109/4 :facepalm:
Original post by thegodofgod
Woops - meant 109/4 :facepalm:


Easy mistake to make. It's generally a good idea to check your answer by plugging your solution into the equation to ensure it works.
Original post by Chwirkytheappleboy
Easy mistake to make. It's generally a good idea to check your answer by plugging your solution into the equation to ensure it works.


I know - but the fact that the square root came out as an integer made me think that I was along the right track :frown:
Reply 7
Avatar for Dr.Pwepper
Dr.Pwepper
OP
4
Thanks guys! I know what I did wrong now. I didn't add 42.25 to both sides of the equation. How do you close this thread haha :biggrin:
It's against the rules to post answers, you're supposed to help users see where they've gone wrong :smile: .
Original post by ViralRiver
It's against the rules to post answers, you're supposed to help users see where they've gone wrong :smile: .


I tend to agree, but I think in this case where it's such a simple question with such a straightforward answer, the best thing to do is just give the solution and then the person who asked the question can just see where they went wrong

Original post by Dr.Pwepper
Thanks guys! I know what I did wrong now. I didn't add 42.25 to both sides of the equation. How do you close this thread haha :biggrin:


Normal users can't close threads, we just let it die

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