1. ## Solving cubic equation

Hi, I am really out of touch with solving these.

$\displaystyle -t^3+10t^2-30t+32$

solving for t.
If I can break it down to a quadratic, I should be able to do it with no problems. But I don't know how to find which factor to take out.
Any help is great!

2. Originally Posted by U-God
Hi, I am really out of touch with solving these.

$\displaystyle -t^3+10t^2-30t+32$

solving for t.
If I can break it down to a quadratic, I should be able to do it with no problems. But I don't know how to find which factor to take out.
Any help is great!
Roots are not real, use a calculator, the other methods will not be easy at all

3. Originally Posted by U-God
Hi, I am really out of touch with solving these.

$\displaystyle -t^3+10t^2-30t+32$

solving for t.
If I can break it down to a quadratic, I should be able to do it with no problems. But I don't know how to find which factor to take out.
Any help is great!
There is only 1 real root and its exact value is found with difficulty using Cardano's method. Why are you trying to solve this cubic, what is the whole question that it has come from?

4. The only real solution can be found using the Newton-Raphson method. If tou have an equation in the form...

$\displaystyle f(x)=0$

... the method consists in searching better approximation of a solution in iterative way as follows...

$\displaystyle x_{n+1} = x_{n} - \frac{f(x_{n})}{f ' (x_{n})}$

In our case is...

$\displaystyle f(x)= x^{3} -10\cdot x^{2} + 30\cdot x -32$

In few itrations you can find the only real solution $\displaystyle x \simeq 5.75110070238\dots$ and after that you can reduce the equation in quadratic form...

Kind regards

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