Question

What adds to 10 and multiplies to -300

Answer 1

X+Y=10
XY=-300

Solve for one of the variables

X=10-Y

Plug into the other equation

Y(10-Y)=-300

Now, you have a quadratic...

-y²-10y+300=0

I would multiply everything by -1, so there's no coefficient on y²

y²+10y-300=0

And solve...

-10±√(100-4(-300))
----------------------------
2

Y=-5±5√(13)

Plug back onto original equation...

X+(-5±5√(13))=10
X±5√(13)=15
X=15±5√(13)

Note: There are 2 sets of answers, keep the negatives with the negatives, and the positives with the positives when dealing with the ±.