First part:

-36 * 2 = -72

-36 + 2 = -34

Second part: Assuming that the 3x^2 is positive. (the answers are bolded)

3x^2-34x-24=0

(x-12)(3x+2)=0

x-12=0 3x+2=0

+12 +12 -2 -2**x=12 ** 3x=-2

\( \frac{3x}{3}= \frac{-2}{3} \)

**x=\( \frac{-2}{3} \)**

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)

what’s funny is that the equation doesn’ help solve the question about what 2 numbers multipyto -72 andadd to -34