xy=-126
x+y=6
minus x
y=6-x
sub
x(6-x)=-126
6x-x^2=-126
minus (6x-x^2) both sides
0=x^2-6x-126
in form
ax^2+bx+c=0
x=[tex] \frac{ -b+/-\sqrt{b^{2}-4ac} }{2a} [/tex]
a=1
b=-6
c=-126
x=[tex] \frac{ -(-6)+/-\sqrt{(-6)^{2}-4(1)(-126)} }{2(1)} [/tex]
x=[tex] \frac{ 6+/-\sqrt{36+504} }{2} [/tex]
x=[tex] \frac{ 6+/-\sqrt{540} }{2} [/tex]
x=[tex] \frac{ 6+/-6\sqrt{150} }{2} [/tex]
x=[tex] 3+/-3\sqrt{150} [/tex]
the numbers are
[tex] 3+3\sqrt{150} [/tex] and [tex] 3-3\sqrt{150} [/tex]
