Anguyennn
  • Anguyennn
how do solve 3x^3+2x^2-12x-8=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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zepdrix
  • zepdrix
Ooo I think this one is going to work out nicely with grouping! :)
Anguyennn
  • Anguyennn
how do you do that?
Anguyennn
  • Anguyennn
yes that is what the question is asking me to do actually haha :)

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zepdrix
  • zepdrix
Oh interesting c: hah
zepdrix
  • zepdrix
\[\large\rm \color{#DD4747}{3x^3-12x}+\color{#3366CF}{2x^2-8}=0\]Notice that the cubic term and the first degree term are both divisible by 3, while the squared term and constant term are both even, divisible by 2, so let's group them like this!
zepdrix
  • zepdrix
We want to do some factoring. What can we factor out of the red guys? What do they have in common?
Anguyennn
  • Anguyennn
\[\large\rm \color{#DD4747}{3x^3-12x}+\color{#3366CF}{2x^2-8}=0\]
Anguyennn
  • Anguyennn
all i see is that
Anguyennn
  • Anguyennn
I don't see any equations
zepdrix
  • zepdrix
The equation didn't show up for you? Are you using Internet Explorer or some junk like that? :c lol
Anguyennn
  • Anguyennn
I am using safari
zepdrix
  • zepdrix
oh boy :( hmm
zepdrix
  • zepdrix
Reload browser? :o Maybe the plugin just crashed for you or something
Anguyennn
  • Anguyennn
ok please hold on ok
Anguyennn
  • Anguyennn
oh yes i see it now!!
zepdrix
  • zepdrix
yay c:
Anguyennn
  • Anguyennn
so it would be (3x+2) (x^2-4)
zepdrix
  • zepdrix
Oh, you did it all the way already XD haha nice!
Anguyennn
  • Anguyennn
so would the final answer be x=2/3, -2, 2?
zepdrix
  • zepdrix
-2/3, ya? :) Gotta subtract the 2 over
Anguyennn
  • Anguyennn
oh!!!
Anguyennn
  • Anguyennn
but wait, what about x^3-8x^2=0
zepdrix
  • zepdrix
Oh this is another problem? I see :)
Anguyennn
  • Anguyennn
this is another one
Anguyennn
  • Anguyennn
yes
zepdrix
  • zepdrix
So they each have at least two x's, multiplying, ya? So we can pull an x^2 out of each.
zepdrix
  • zepdrix
\[\large\rm x^2(x-8)=0\]Something like that, ya? :d
Anguyennn
  • Anguyennn
yes
zepdrix
  • zepdrix
Apply your `Zero-Factor Property` again :) \(\large\rm x^2=0\) and \(\large\rm x-8=0\) and solve for x in each case.
Anguyennn
  • Anguyennn
I know one of them would be x=8
Anguyennn
  • Anguyennn
but what about for the x^2? that is what i am confused about
zepdrix
  • zepdrix
\(\large\rm x^2=0\) Take square root, \(\large\rm \pm x=0\) Leading to, \(\large\rm x=0\)
zepdrix
  • zepdrix
square root of zero is... zero :) ya?
Anguyennn
  • Anguyennn
yes
Anguyennn
  • Anguyennn
but when you square root x it becomes 10
zepdrix
  • zepdrix
?
Anguyennn
  • Anguyennn
oh wait never mind, i am talking nonsense
zepdrix
  • zepdrix
x is being squared. we perform the `opposite` operation of squaring to remove the square. square root is the opposite of squaring. So when we apply the square root, they `undo` one another.
Anguyennn
  • Anguyennn
wow thanks I understand it now!!
zepdrix
  • zepdrix
yay team \c:/
Anguyennn
  • Anguyennn
are you able to help me with some other questions since you are here already :P
Anguyennn
  • Anguyennn
you are a really great help btw thank you i appreciate it
zepdrix
  • zepdrix
uh sure +_+
zepdrix
  • zepdrix
you can post it, i gotta make some food real quick :D brb
Anguyennn
  • Anguyennn
1 Attachment
Anguyennn
  • Anguyennn
1 Attachment
Anguyennn
  • Anguyennn
I am not sure how to do c, f, or g.
zepdrix
  • zepdrix
What did you get for b? Your profit function.
Anguyennn
  • Anguyennn
I got 13.83n-102.4
Anguyennn
  • Anguyennn
I showed you a picture as well
Anguyennn
  • Anguyennn
the second document
zepdrix
  • zepdrix
oh lol :)
Anguyennn
  • Anguyennn
yup :)
zepdrix
  • zepdrix
Since this is a `linear function`, \(\large\rm \text{rate of change = slope}\) So the slope of your P(n) function is your rate of change.
Anguyennn
  • Anguyennn
how do you find out the slope? mx+b?
zepdrix
  • zepdrix
Yes, m :)
zepdrix
  • zepdrix
We can write the number like this if it makes things easier:\[\large\rm m=\frac{13.83}{1}\]Remember that slope is `rise over run`. So I would like two separate numerical values in my slope so I can interpret it. The 13.83 represents profit, the 1 represents 1 pizza sold. So this value represents the amount of profit made per pizza!
Anguyennn
  • Anguyennn
hmm
Anguyennn
  • Anguyennn
so would 1 be the y coordinate on the graph?
zepdrix
  • zepdrix
slope is `change in y` divided by `change in x`. So the bottom number is the x ( n in this case ).
Anguyennn
  • Anguyennn
oh ok thank you so much for your help!
Anguyennn
  • Anguyennn
until next time :)
zepdrix
  • zepdrix
`practical domain` You don't want to open a pizza shop and sell two pizzas every day. You'll end up losing money because of your operating costs! So you want your domain to start from the `break-even point`.
Anguyennn
  • Anguyennn
which is going to be n=7.40?

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