To Reiny:

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!

Hi. I've seen your previous post. I'll try answering them. :)

(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

(9n+1)^2 = 9

9n + 1 =-+ 3

9n +1 = -3

9n. = -4

n = -4/9

9n + 1 = 3

9n = 2
n = 2/9

-4/9, 2/9

Hello! No problem at all, I'd be happy to help you with the corrected equation.

The equation you provided is (9n + 1)^2 = 9. To solve this equation, we'll first simplify the equation using the exponent rule that says (x^a)^b = x^(a*b). Applying this rule, we get:

(9n + 1)^2 = 9
(9n + 1)(9n + 1) = 9

Now, we'll expand the equation by multiplying the terms:

(81n^2 + 18n + 1) = 9

Next, let's move all the terms to one side to obtain a quadratic equation:

81n^2 + 18n + 1 - 9 = 0
81n^2 + 18n - 8 = 0

To solve this quadratic equation, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions x can be found using:

x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values for a, b, and c from our equation, we get:

n = (-18 ± √(18^2 - 4 * 81 * -8)) / (2 * 81)

Now, let's simplify and calculate the value:

n = (-18 ± √(324 + 2592)) / 162
n = (-18 ± √(2916)) / 162
n = (-18 ± 54) / 162

Now we can solve for two possible values of n:

n = (-18 + 54) / 162
n = 36 / 162
n ≈ 0.222

n = (-18 - 54) / 162
n = -72 / 162
n ≈ -0.444

So the two solutions to the equation (9n + 1)^2 = 9 are approximately 0.222 and -0.444.

Regarding the sign you mentioned, the "check mark" symbol (√) refers to the square root operation. In mathematics, the square root (√) of a number is a value that, when multiplied by itself, gives the original number. For example, √4 = 2, since 2 * 2 = 4.

I hope this helps! Let me know if you have any further questions or if there's anything else I can assist you with.