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[Seriouslyfunny]

Bro why even do the algebra if you can already come up with 100 = 125 - 25 😂

[jellyfrancis]

Quadratic equation is good to go rather than cubic and when you guessed 5 is a root and you can use it and factor as x-5 times a quadratic rather than this hardly factory ❤️⚡

[PiotrBaczek]

I solved it using the Horner's method.

[fifiwoof]

Where does 125-25 come from? HUGE LEAP! EXPLAIN PLEASE!

[ichdu]

Too long and too tricky method here. Ever heard of long division or polynomial division?

Step 1 one solution is X=5. Maybe proof this, if necessary.
Step 2 you divide (x^3 - x^2 - 100):(x - 5) and receive the quadratic equation
Step 3 solve the quadratic equation --> ready.

[knotwilg]

you don't explain how you magically come up with the idea of splitting 100 in 125-25

the key point is to ASSUME there are whole solutions for x

In that case we can factorize x³-x² = x²(x-1). The only squares dividing 100 are 1, 4, 25 and 100. And we can quickly verify that one of these gives a solution: x=5. Then you can factor out x-5 of x³-x²-100 through Horner, or using the trick you used, to reduce the cubic equation to a square equation and verify using the easier standard method that this has no real solutions.

In general though, there are no whole solutions and you can only apply the formula for cubic equations, which is not an easy one to learn by heart.