x+y=3
xy=-30
x+y=3
minusx
y=3-x
sub
x(3-x)=-30
3x-x^2=-30
times -1 both sides
x^2-3x=30
minus 30 both sides
x^2-3x-30=0
use quadratic
for
ax^2+bx+c=0
x=\(\frac{-b+/- \sqrt{b^2-4ac} }{2a}\)
1x^2-3x-30=0
a=1
b=-3
c=-30
x=\(\frac{-(-3)+/- \sqrt{(-3)^2-4(1)(-30)} }{2(1)}\)
x=\(\frac{3+/- \sqrt{9+120} }{2}\)
x=\(\frac{3+/- \sqrt{129} }{2}\)
the numbers are \(\frac{3+ \sqrt{129} }{2}\) and \(\frac{3- \sqrt{129} }{2}\)
