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Hint : (16)(-5) = -80 16 + -5 = 11
As a start, split the middle term as `16x - 5x`
0 = -2x^2 + `11x` + 40 = -2x^2 + `16x-5x` + 40
wow i would have never thought of that!
knw how to finish it off ?
how did you figure that out?
yeah i can finish it off but i'm intrigued on how you found those numbers
basically we need to find two integers such that they multiply to `(40)*(-2)` and add up to the coefficient of middle term `11`
so you look at the factors of 40*2 : 40*2 = 10*4*2 = 5*2^4 = 5*16 and you see that 16 and -5 are the magic numbers
Wow thanks so much!
quadratic formula is always there if you don't like to do all that
yeah of course I know that, haha
but It seemed like there was a shorter way so I asked
But really appreciate your work.
im not sure if we can say that factor by grouping is any shorter than using the quadratic formula directly... factor by grouping doesn't work always, it works only when the roots are rational
usually i try factor by grouping first, if it doesn't work then i use quadratic formula..