Posted by **Brandi** on Sunday, November 3, 2013 at 9:48pm.

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

- Math -
**Reiny**, Sunday, November 3, 2013 at 9:56pm
(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

- Math -
**Brandi**, Sunday, November 3, 2013 at 10:16pm
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!

- Math -
**Jai**, Sunday, November 3, 2013 at 11:04pm
(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

- Math -
**Steve**, Sunday, November 3, 2013 at 11:39pm
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 = ±3-1

9n = -4,2

n = -4/9,2/9

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