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How many ways can a quadratic equation of $ax^2+bx+c=0$ be solved?

The most common one I know is the quadratic formula and factorization method.

$x=\frac{-b+\sqrt{b^2+4ac}}{2a}$

and $(ax+b)(cx+d)=0$

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  • $\begingroup$ aplustopper.com/factorization-by-splitting-middle-term $\endgroup$ – lab bhattacharjee Apr 19 at 10:57
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    $\begingroup$ another alternative is by completing the square for those quadratics that don't factorise cleanly by inspection. generally though, the quadratic formula is the best way. $\endgroup$ – thesmallprint Apr 19 at 10:57
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    $\begingroup$ How do you solve the equation $x^2+3x+1=0$ through the “factorization method”? $\endgroup$ – José Carlos Santos Apr 19 at 10:58
  • $\begingroup$ The radicand must be $$b^2-4ac$$ $\endgroup$ – Dr. Sonnhard Graubner Apr 19 at 11:17
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    $\begingroup$ You have printed the quadratic formula incorrectly, More broadly, I'd expect that various methods that work in general end up being more or less equivalent to the quadratic formula. Certainly, completing the squares is. There are numerical methods of course...Newton's is quite effective for quadratics. But these just approximate the relevant square root. $\endgroup$ – lulu Apr 19 at 11:25

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