Question

What numbers add to 32 and multiply to -80??

Answer 1

X+y=32
xy=-80

x+y=32
minus x both sides
y=32-x
sub for y

x(32-x)=-80
32x-x^2=-80
times both sides by -1
x^2-32x=80
minus 80 both sides
x^2-32x-80=0
use quadratic formula
where
ax^2+bx+c=0
x=$\frac{-b+/- \sqrt{b^2-4ac} }{2a}$

a=1
b=-32
c=-80

x=$\frac{-(-32)+/- \sqrt{(-32)^2-4(1)(-80)} }{2(1)}$
x=$\frac{32+/- \sqrt{1024+320} }{2}$
x=$\frac{32+/- \sqrt{1344} }{2}$
x=$\frac{32+/- 8\sqrt{21} }{2}$
x=16+/-4√21

the numbers are
16+4√21 and 16-4√21