Solve this please! Will medal for giving an answer!!!

0=-2x^2+11x+40

Question

Solve this please! Will medal for giving an answer!!!

0=-2x^2+11x+40

ganeshie8 · Answer

Hint :  

(16)(-5) = -80

16 + -5 = 11

ganeshie8 · Answer

As a start, split the middle term as `16x - 5x`

ganeshie8 · Answer

0 = -2x^2 + `11x` + 40

   = -2x^2 + `16x-5x` + 40

anonymous · Answer

wow i would have never thought of that!

ganeshie8 · Answer

knw how to finish it off ?

anonymous · Answer

how did you figure that out?

anonymous · Answer

yeah i can finish it off but i'm intrigued on how you found those numbers

ganeshie8 · Answer

basically we need to find two integers such that they multiply to  `(40)*(-2)` 
and add up to the coefficient of middle term `11`

ganeshie8 · Answer

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

anonymous · Answer

Wow thanks so much!

ganeshie8 · Answer

quadratic formula is always there if you don't like to do all that

ganeshie8 · Answer

|dw:1440046082224:dw|

anonymous · Answer

yeah of course I know that, haha

anonymous · Answer

but It seemed like there was a shorter way so I asked

anonymous · Answer

But really appreciate your work.

ganeshie8 · Answer

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

ganeshie8 · Answer

usually i try factor by grouping first, if it doesn't work then i use quadratic formula..