OK SO THE THING WE HAVE TO FACTOR DOESN"T RELATE TO THE PROBLEM
easy way to solve is factor -72 and find what factos add up so 34
-72=
1,-72=-71 no
2,-36=-34 correct
therefor the numbers are 2 and -36
that was easy
now the legit math way
so
xy=-72
x+y=-34
x+y=-34
subtract x
y=-34-x
subsitute
x(-34-x)=-72
-34x-x^2=-72
add 34x+x^2 to bboth sides
0=x^2+34x-72
factor
facotr -72 and find what 2 factors add up to 34
-2 and 36 add up to 34
(x-2)(x+36)=0
set each to zero
x-2=0
add 2
x=2
x+36=0
subtract 36
x=-36
the numbers are 2 and -36
Second question
factor 3x^2-34x-24 which has nothing to do with the problem except ahthat 3 times 24=72
we do is we factor the first term
3=1 times 3
we know that it will be in a form liike
(somethingx+something)(somethingx+something) so
we put the 1 and 3 for the first somethings
(3x+ something)(1x+something)
then we factor 24
24=1 and 24 or 2 and 12 or 3 and 8 or 4 and 6
let's pick a random pair
2 and 12
they have to be different signs since the last term is negative
since midlde term is also negative, we know that bigge number is negative so
(3x+2)(x-12)
we expand
3x^2+2x-36x-24
3x^2-34x-24
ok, so I don't know what the equiqation was for but
numbers are 2 and -36
facotre form of equation that didn't relate=(3x+2)(x-12)
