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 = ±3-1
9n = -4,2
n = -4/9,2/9
(81n^3+18n^2-62n+3)/(9n+1)
Of course! I'm here to help you understand how to solve these problems on your own. Let's go through each question step by step:
1. Solve the equation: (9n + 1)^2 = 0
To solve this equation, we need to take the square root of both sides because the square root of zero is still zero:
√((9n + 1)^2) = √0
Simplifying this, we get:
9n + 1 = 0
Now, let's isolate the variable 'n' by subtracting 1 from both sides:
9n = -1
Finally, divide both sides by 9 to solve for 'n':
n = -1/9
Therefore, the solution to the equation is n = -1/9.
2. Solve the equation by completing the square: x^2 + x + 7 = 0
To solve this equation by completing the square, we need to follow these steps:
Step 1: Make sure the leading coefficient of the quadratic term (x^2) is 1. In this equation, it is already 1, so we can proceed.
Step 2: Take half of the coefficient of the linear term (x) and square it. Then, add this value to both sides of the equation. In this case, the coefficient of x is 1, so half of it is 1/2. When squared, (1/2)^2 = 1/4. Adding 1/4 to both sides, we get:
x^2 + x + 1/4 = -7 + 1/4
Simplifying this, we have:
(x + 1/2)^2 = -27/4
Step 3: Take the square root of both sides to isolate x + 1/2:
√((x + 1/2)^2) = √(-27/4)
Now, we have two possible solutions:
x + 1/2 = √(-27/4) or x + 1/2 = -√(-27/4)
Step 4: Simplify and solve for x. Since the square root of a negative number is imaginary, we know that this equation has no real solutions.
Therefore, the equation x^2 + x + 7 = 0 has no real solutions.
I hope this explanation helps you understand the process of solving these equations! Let me know if you have any further questions.