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=
`(-b+/- √(b^2-4ac) )/(2a)`

a=1
b=-32
c=-80

x=
`(-(-32)+/- √((-32)^2-4(1)(-80)) )/(2(1))`
x=
`(32+/- √(1024+320) )/(2)`
x=
`(32+/- √(1344) )/(2)`
x=
`(32+/- 8√(21) )/(2)`
x=16+/-4√21

the numbers are
16+4√21 and 16-4√21