What times what equals - 72 but also adds up to - 1. Factor quadratic expressions

Answer: 8 and - 9

Step-by-step explanation: Let x be the first number we are looking for and y the second number.

We know that x*y=-72

Also we know that x+y=-1 from this x=-1-y

Subtitue x to the first equation to get:

(-1-y) * y=-72

-y^2-y=-72

0=y^2 + y - 72

To solve it with factor method we use that 72=8*9 and 9-8=1

y^2+y-72 = (y-8) (y+9) = 0

Thus y=8 or y=-9

x=-1-y from above

Thus x=-9 or x=8

Lets check if y=8 and x=-9 than 8*-9=-72 and 8 + (-9) = -1

The same is true for the above pair as it is the same solution just x and y switched.