Question

What two numbers add to 8 and multiply to 28

Answer 1

find numbers that multiply to 28 and add them to see if they add to 8
28=
1 and 28=29 not 8
2 and 14=16 not 8
4 and 7=11 not 8
that's it'
no 2 numbers
we must use quadratic formula

x+y=8
xy=28

x+y=8
subtract x fromb oths ides
y=8-x
subsitute
x(8-x)=28
distribute
8x-x^2=28
add x^2 to both sides
8x=28+x^2
subtract 8x
x^2-8x+28=0

if you have
ax^2+bx+c=0 then x=
`\frac{-b+/- \sqrt{b^(2)-4ac} }{2a}`
so if we have
1x^2-8+28=0 then
a=1
b=-8
c=28

x=
`\frac{-(-8)+/- \sqrt{(-8)^(2)-4(1)(28)} }{2(1)}`
x=
`(8+/- √(-48) )/(2)`
x=
`(8+/- 4 √(-3) )/(2)`
x=
`4+/- 2 √(-3)`
x=
`4+/- 2i √(3)`
there are no real numbers that satisfy this