Question

What numbers add to 18 anf multiply to -47

Answer 1

factor -47
it's prime
we have to use quadratic

so
set equations
x+y=18
xy=-47


x+y=18
minus x from both sides
y=18-x

sub 18-x for y in other equatin

x(18-x)=-47
distribute
18x-x^2=-47
times both sides by -1
x^2-18x=47
minus 47 from both sides
1x^2-18x-47=0

for equation
ax^2+bx+c=0
x=
`(-b+/- √(b^2-4ac) )/(2a)`


a=1
b=-18
c=-47

x=
`(-(-18)+/- √((-18)^2-4(1)(-47)) )/(2(1))`
x=
`(18+/- √(324+188) )/(2)`
x=
`(18+/- 16√(2) )/(2)`
x=9+/-8√2

the numbers are
9+8√2 and 9-8√2