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
