Question

How do I find the solutions of this equation....

Answer 1

x^3-14x^2+40x-192

Answer 2

To start you have to do this:

x^3-14x^2+40x-192 = 0

Now you solve for x.
Does this help?

Answer 3

a little yes thanks

Answer 4

Did you go over factor by grouping or polynomial long division? Both of those are tactics that might help with that problem.

Answer 5

um I never heard of the long division method O.o
i thought this required multiplying but idk where to start :/
I need help finding x (step by step)

Answer 6

Well, you have to find something you can factor. Gettig the factors gets you the solution. When it is a trinomial, the finding things that multiply and add is probably what you are used to. However, this has 4 terms, so it makes it a little harder. That is where the grouping comes in.

Answer 7

Can you show me what u mean like write it out?

Answer 8

like how i would do it.....

Answer 9

Trying. Not the easiest one, I'll tell you that!

Answer 10

OK: I started with seeing what things multiply to become 192. If I am going to factor anything out, it has to related to that last term. All these things multiply togeether to equal 192:

96*2
64*3
48*4
32*6
24*8
12*16

Now that I have a list of things, I need to see if any of them make sense for other parts of what I factor out.

Answer 11

Now, the make sense part largey comes down to the x term. You have +40x. So whatever I add together when I get the x term, has to come to +40x. With a trinomial, this is pretty easy. However, this is 4 terms, so it might be a little more tricky.

Answer 12

AH HA! 40 = 2(12)+16 or 40 = 24 +2(8)

So those last two groups of numbers look likt they might work out. They can both do combinations that give me the 40x, and they both relate to getting my -192. Also, because both the -192 and -14x^2 are negative, I know I am going to have multiple negatives in here somewhere.

Yah, this one is not that easy. Hmm. If I had it available for doing this, I would use a poly solver and work backwards! Even a graph and work backwards from that would help with this one.

Answer 13

At this point I would have to brute force it using this method. Polynomeal division might have been easier, but you said you have not gotten to that yet.

Answer 14

yes

Answer 15

Question though what do u mean by "brute force?"

Answer 16

Trying things and seeing if they make sense. Not having much luck. I am trying some division at this point since I have 24, 8, 12, and 16 as likely suspects. I am not sure why you would have \(x^3-14x^2+40x-192\) before getting into dividing polynomials. I do not see much other coice for getting the answer.

Answer 17

OK. Through division I got to: \((x-12)(x^2-2x+16)
\). That second part does not look like an easy factor, so it would need the quadratic formula.

Answer 18

Are you allowed to use a calculator to help solve it?

Answer 19

Yah, a calculator to get the basics down would really have helped with this one!

Answer 20

Well I wasn't told i couldn't

Answer 21

So, hmmm.... no using a calculator at all or, they just wanted the accurate answers and not a calculator approximation?

Answer 22

no I can use it! casue I think the answer is supposed to be in decimal form

Answer 23

Then use one :P

Answer 24

ell, if the calculator has a poly solver, that would certainly have heled. It would have let you know that (x-12) was a factor. What I did at the start is above. I found things that would divide into that -192. From knowing that those had to be related to 40, I found a few that were. Then, based off those two bits of information, I made a small list of things to try dividing out. But I don't know how you would do this one without either synthetic division or polynomeal long division. That is what I used next to het me to the (x-12) as a factor.
So I got \((x-12)(x^2-2x+16)\), which tells em 12 is one solution for x. The \((x^2-2x+16)\) part I think needs the quadratic formula.
The exact process I used is listed here: http://www.purplemath.com/modules/solvpoly.htm

Sorry, but I don't have an easy step by step with this one! It was a little more complex than I expected.

Answer 25

No problem your explanation so far has helped a lot

Answer 26

Well, I think you have a form you can solve at this point, if you know the quadratic formula.

Answer 27

Thanks again!

Answer 28

np. Don't have too much fun!

Answer 29

Oh, and that Purple Math site has a lot of very well done explanations. I used them a lot as an additon to my math book. The book would say it one way, Purple Math another, and between the two I could generally work it out.

Answer 30

Thanks!