so xy=-29 and x+y=1 subtract x from both sides y=1-x subsitute 1-x for y in first equation x(1-x)=-29 distribute x-x^2=-29 add x^2 to both sides x=-29+x^2 subtract x from both sides 0=x^2-x-29 so we can use the quadratic formula to solve for x if the equation=0 and it is in ax^2+bx+c form so
if ax+bx+c=0 then x=[tex] \frac{ -b+/-\sqrt{b^2-4ac} }{2a} [/tex] that means x=[tex]\frac{ -b-\sqrt{b^2-4ac} }{2a}[/tex] or x=[tex] \frac{ -b-\sqrt{b^2-4ac} }{2a} [/tex] so
the second number is [tex]\frac{ -(-1)+\sqrt{-1^2-4(1)(-29)} }{2(1)}=\frac{ +1+\sqrt{1^2+(-116)} }{2(1)}= \frac{1+10.816653826392}{2} = \frac{ +1+\sqrt{117} }{2}= \frac{10.816653826392}{2}=5.908326913196[/tex]
the two numbers are 5.908326913196 and -4.908326913196
