u^2-9u+20=0

Question

I am supposed to solve for u.  I was hoping to see the work so that I would better understand how to get the answer.

Answer 1

u²-9u+20=0

you want 2 numbers whose product is 20 and whose sum is 9 (worry about the signs later)

look at the factors of 20

1*20

2*10

4*5 !!!   4+5=9

(u   )(u   ) so far...

20 is positive so 4 and 5 both have to be positive or both negative

-9 is negative (obviously)

therefore 4 and 5 must both be negative

(u-4)(u-5)=0

u-4=0

u=4

u-5=0

u=5