myrmepropagandist on Nostr: 6x²-13x-5=0 ax²+bx+c=0 This is why it's called the AC method: Look for factors of ...

6x²-13x-5=0
ax²+bx+c=0

This is why it's called the AC method:

Look for factors of
a*c = -30 that will add to the pernicious middle term (b=-13)

This will make factoring by grouping possible.

factors of 30:

1*30
2*15
3*10
5*6

2 and 15 can get us to -13!

So we write -13x=-15x+2x and plug it into:

6x²-13x-5=0

6x²-15x+2x-5=0

3x(2x-5)+(2x-5)=0 grouping

(2x-5)(3x+1)=0 factoring

And the roots are 5/2 and -1/3

Easier than completing the square and no guessing.

8/8 Fin!~