Math
posted by Brandi on .
The following are the last two problems on my test review. I am trying to study for a test. This is not my homework. I am not expecting anyone to do my homework for me. I just need to get the answers to be able to study and if you can help, I would really really appreciate it!
1. solve the equation. (9n+1)squared=0
2. solve the equation by completing the square. xsquared+x+7=0

(9n+1)^2 = 0
9n+1 = 0
9n = 1
n = 1/9
x^2 + x = 7
x^2 + x + 1/4 = 7 + 1/4
(x+1/2)^ = 27/4
x+1 = ± √27 /2
x = 1 ±3i√3/2
= (2 ± 3i√3)/2 
Hi, thank you for your time Reiny and your info. I am so sorry but on the first one I accidentally put 0 where I should have put =9. In other words, the first equation should have said (9n+1)squared =9. Really sorry to have taken up your time with the wrong equation, but if you are able to help me out again, with the right one, I would appreciate it. Also, I am unfamiliar with the sign you use that looks like a check mark, could you please advise what the sign means? Thanks for your help!

(9n+1)squared = 9
We expand the term with the square:
(81n^2 + 18n + 1) = 9
81n^2 + 18n + 1  9 = 0
81n^2 + 18n  8 = 0
Factoring,
(9n + 4)(9n  2) = 0
n = 4/9 and n = 2/9
Note that there are two values of n.
The sign that looks like a check mark in #2 is a squareroot sign.
I'm not Reiny but I hope you can trust my answer.
Hope this helps :3 
The answer is good, but it might have been a lot simpler to solve it the way Reiny did:
(9n+1)^2 = 9
9n+1 = ±3
9n = ±31
9n = 4,2
n = 4/9,2/9 
(81n^3+18n^262n+3)/(9n+1)