so x times y=15 x+y=12 solve x+y=12 subtract x from both sides y=12-x subsitute xy=15 x(12-x)=15 distribute 12x-x^2=15 subtract (12x-x^2) from both sides 0=x^2-12x+15 use quadratic formula which is x=[tex] \frac{ -b+/- \sqrt{b^{2}-4ac} }{2a} [/tex] where you have 0=ax^2+bx+c so a=1 b=-12 c=15 subsitute x=[tex] \frac{ -(-12)+/- \sqrt{-12^{2}-4(1)(15)} }{2(1)} [/tex] x=[tex] \frac{ 12+/- \sqrt{144-60} }{2} [/tex] x=[tex] \frac{ 12+/- \sqrt{84} }{2} [/tex] x=[tex] \frac{ 12+/- 2\sqrt{21} }{2} [/tex] x=6+/- [tex] \sqrt{21}[/tex] x=6+ [tex]\sqrt{21}[/tex] or 6- [tex] \sqrt{21} [/tex] or aprox x=10.5826 or 1.41742 the numbers are 10.5826 and 1.41742
