What multiplies to 6 but adds to 17

The answer is -4 and 21

I am glad to help!

You can write this line as the system:

x + y = 17
xy = 6

To solve it, you first need to get the proper value of either x or y. In this case i choose to get the value of x:

x + y = 17
x = 17-y

With this, i an input the value into the second line:

(17-y)y = 6

17y-y^2=6

-y^2+17y-6=0
can be solved with the quadratic formula.

y = (-17 +/- sqrt(-17^2 - 4*-1*-6))/2*-1
y = (-17 +/- sqrt(289 - 24)/-2
The square root is 16.28
y = (-17 +/- 16,28)/-2
y_1 = (-17 + 16.28)/-2 = 0,36
y_2 = (-17 - 16.28)/-2 = 16,64

To skip the work ahead of us, x_1 and x_2 will end up with the exact same numbers, as we could multiply both ways.

The numbers are ca. 0,36 and 16,64

0,36+16,64 = 17

0,36*16,64 = 5,999997 = ca. 6

Sorry for the small amount of rounding, but i hope this works.