500 years of NOT teaching THE CUBIC FORMULA. What is it they think you can't handle?

What people said

Strong rec JMoravitz · 2019-12 · Mathematics Stack Exchange · on “How to solve this cubic equation? $x^3 -3x^2+ 4 = 0 $”

There are general ways of approaching factoring a cubic. This video [this video] provided a great explanation that I thoroughly enjoyed, making me agree with the creator that not teaching the cubic formula in schools for so long has probably been a great disservice since the technique in deriving the formula seems so useful. That said, I can understand not teaching it on the grounds that factoring cubics is not something that comes up regularly in physics and geometric applications.

Recommends D. Ungaretti · 2019-09 · Mathematics Stack Exchange · on “Find a general formula for a tangent to a cubic which, is also normal to the cubic at the second intersection”

Finally, I strongly suggest you to watch a recent video of the Mathologer channel [this video] that talks precisely about the derivation of solutions to a cubic polynomial.

Recommends JMoravitz · 2020-02 · Mathematics Stack Exchange · on “How to factor a simple algebraic expression?”

The most generalized approach to factoring a cubic that is commonly used is called Cardano's Formula. This Mathologer [this video] video is well worth watching from the beginning for anyone even mildly interested in this, but if you just want a quick answer you might just care about watching from where I timestamped. Reading about it instead at proof wiki [LINK] can also help.

Recommends Jivan Pal · 2020-03 · Mathematics Stack Exchange · on “Why is the "solving for cubic equation roots general rule" sometimes not applicable while the equation obviously has roots?”

For more insight into the history and derivation of the Cardano formula, and how complex numbers were treated at the time of Tartaglia's discovery with an attitude of "that's not legitimate!", see this video [this video] .

Recommends JMoravitz · 2020-04 · Mathematics Stack Exchange · on “Factorize $x^4 + x^3 - 3x^2 - 4x - 4$ showing all work”

For the fully generalized problem, I recommend this video by Mathologer [this video] . It is a bit long, but it was the first time that an explanation of factoring a cubic made sense to me.

Recommends Arthur · 2020-12 · Mathematics Stack Exchange · on “Who found the proof for the quartic formula?”

In this video [this video] , Mathologer shows how one solves the cubic equation. Then at the very end how you use that to solve the quartic in just a few minutes. Have a look. Spoiler: No one found _that_ formula. They simplified the problem, solved the simplified problem, then transformed back. Note how many terms and expressions in your formulas are basically the same, only with a sign change here and there. That's the result of _loads_ of simplifying substitutions.

Recommends Knoquer Bonk · 2021-12 · Mathematics Stack Exchange · on “I'm failing to solve a cubic equation”

SOLUTION: Because I made the substition of $t = x + \frac {b}{3a}$ , I had to substract $\frac {b}{3a}$ from my final answer, giving me the formula for x: $x = u + v - \frac {b}{3a}$ . I'm trying to write my own cubic equation solver program using C#, but I am getting the wrong answer. I'm pretty sure all my code is correct, so I suspect I'm doing something wrong with the calculations itself. I suspect I'm just missing a step or made a fundamental mistake in solving the cubic equation. Please keep in mind I have never solved a cubic equation before. I will thoroughly explain all the steps I have taken, in the hopes of you finding the mistake. First, I depressed the cubic from the standard fo

Recommends user1031083 · 2022-03 · Mathematics Stack Exchange · on “solve this formula for $x$: $y = \frac{5x(2x^2 + 27x + 89)}{6}$”

Now, I will tried to answer all of your question: Question 1 : Is there a simpler formula solved for x? It really depends on how you want to solve this kind on the problems. You can solve it using general Cubic formula from this great video from Mathologer [this video] . In some cases, you can try to input some small numbers and hopefully you will get a root (cubic polynomial will have at least one real root). Then, use long division to solve other two roots. Question 2 : Why are there 3 ,x = in the formula in the attached image? It is because cubic polynomial will have three roots where it should have a least one real roots. Question 3 : What is I which is present 2 times in front of the Roots i

Recommends Suzu Hirose · 2022-08 · Mathematics Stack Exchange · on “Real solutions to the depressed cubic equation”

I don't know if you like video materials but this by "mathologer" contains a good explanation with graphics etc. [this video]

Recommends Benjamin Wang · 2022-11 · Mathematics Stack Exchange · on “Spivak, Ch, 25, 2(v): Is there some specific technique to factorize $x^3-x^2-x-2$ or must one guess that 2 is root?”

Using the rational root theorem [LINK] on the above cubic, you only need to check whether $\pm 1,\pm2$ are roots. Otherwise there's no rational root and the problem is a little harder. In those cases you'd usually have to use the cubic formula or some simplified version thereof. But thankfully they don't usually come up in exams. This Mathologer video on the cubic equation [this video] may dispel some fears that it is "super complicated".