X^2 - 19x + 90 = 0 Factor and solve

Find what 2 numbers multiply to get 90 and add to get - 19

they must be both be negative so

factor 90

90

1,90

2,45

3,30

5,18

9,10

add

1+90=91

2+45=47

3+30=33

5+18=23

9+10=19 correct

numbers are - 9 and - 10 since negative times negative=positive

so

it factored out to

(x-9) (x-10) = 0

set each to zero

x-9=0

add 9

x=9

x-10=0

add 10

x=10

x=9 or 10