How to split large numbers easily for factoring the middle term?

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I was doing a problem when I got suddenly stuck with a middle term factorisation.

The equation is as follows:

$$x^4-289x^2+14400=0.$$

I managed to somehow solve it, but it took a lot of time.

Can you please help me with a fast way if any, or can you at least tell me what is the fastest method you know?

Thank you.

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1 Answer

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A direct method would be to let $y=x^2$,

and solve $y^2-289y+14400=0$ using the quadratic formula.

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