xy=10
x+y=29
subtract x from both sides for second equation
y=-x-29
subsitute in second equaiton
x(-x-29)=10
-x^2-29x=10
add x^2+29x to both sides
x^2+29x+10=0
quadratic formula
if you have
ax^2+bx+c=0,
x=[tex] \frac{-b+/- \sqrt{b^{2}-4ac} }{2a} [/tex]
so
x^2+29x+10=0
a=1
b=29
c=10
x=[tex] \frac{-29+/- \sqrt{(-29)^{2}-4(1)(10)} }{2(1)} [/tex]
x= [tex] \frac{-29+/- \sqrt{841-40} }{2} [/tex]
x= [tex] \frac{-29+/- \sqrt{801} }{2} [/tex]
x= [tex] \frac{-29+/- 3\sqrt{89} }{2} [/tex]
x= [tex] \frac{-29- 3\sqrt{89} }{2} [/tex] or [tex] \frac{-29+ 3\sqrt{89} }{2} [/tex]
those are the 2 numbers
aprox=-28.65 and -0.349
