solve x
x(x-3)+1=-55/x

Question

solve x
x(x-3)+1=-55/x

anonymous · Answer

I got to x^2 - 3x=-55/x  -1

anonymous · Answer

thanks for viewing

callisto · Answer

Is the question $x(x-3)+1=\frac{-55}{x}$?

anonymous · Answer

yes

callisto · Answer

So, first multiply both sides by x
$$x[x(x-3)+1]=x(\frac{-55}{x})$$$$x^2(x-3)+1(x)=-55$$Simplify it. $$x^3-3x^2+x=-55$$$$x^3-3x^2+x+55=0$$Well... you need to solve this :|

anonymous · Answer

the original equation is x^3  -  3x^2  +x  +55=0

callisto · Answer

Hmm... Sorry :S

anonymous · Answer

without help of calculator doing every thing for you.

anonymous · Answer

it's ok.

anonymous · Answer

hhh see this http://en.wikipedia.org/wiki/Cubic_function

anonymous · Answer

help me|dw:1345083860295:dw|

anonymous · Answer

why

anonymous · Answer

@Callisto 

The equation is

$$\large x^3−3x^2+x+55=0
 $$ ?

callisto · Answer

Yup.

anonymous · Answer

I would only know how to solve this with the newton iteration method.

swissgirl · Answer

The guy is offline neways

anonymous · Answer

I somehow doubt that they require a solution to the question given, except the topic is algorithms.

callisto · Answer

I don't know how to solve these problems when factor theorem doesn't work, at least I haven't learnt to solve this yet...

anonymous · Answer

There isn't a simple way, besides algorithms.

Newton method (easy to derive by the way)

$$\Large x_{n+1}=x_n- \frac{f(x_n)}{f'(x_n)} $$

anonymous · Answer

$$ \Large x_{n+1}= \frac{x(3x^2-6x+1)-(x^3-3x^2+x+55)}{3x^2-6x+1}$$
So

$$\Large = \frac{2x^3-3x^2-55}{3x^2-6x+1} $$

anonymous · Answer

$$f(-1)=6 \f(6)=-4.10344 \
f(-4.10344)=-3.20093 \ f(-3.20093)=-2.97957 $$

anonymous · Answer

$$f(-2.97057)=-2.95607 $$

Guess Wolfram doesn't approach it closer.

callisto · Answer

Wolf gives something.... complicated.

anonymous · Answer

I see identical answers on wolf and here.

anonymous · Answer

ah I think I know what you mean now, when wolf computes the exact answer it will look different of course.

callisto · Answer

You're right :|
I think it takes long time for me to learn this new concept. Thanks for helping :)

anonymous · Answer

You're welcome! 

If you want to learn more about it, you can easily find a lot of explanations all through the internet, it's one of the most common algorithms for approaching solutions. It's actually a pretty straightforward concept, unlike the solution for cubic equations which also have a formula (-: