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
