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=\(\frac{ -b+/- \sqrt{b^{2}-4ac} }{2a}\)
where you have
0=ax^2+bx+c
so
a=1
b=-12
c=15
subsitute
x=\(\frac{ -(-12)+/- \sqrt{-12^{2}-4(1)(15)} }{2(1)}\)
x=\(\frac{ 12+/- \sqrt{144-60} }{2}\)
x=\(\frac{ 12+/- \sqrt{84} }{2}\)
x=\(\frac{ 12+/- 2\sqrt{21} }{2}\)
x=6+/- \(\sqrt{21}\)
x=6+ \(\sqrt{21}\) or 6- \(\sqrt{21}\) or aprox
x=10.5826 or 1.41742
the numbers are 10.5826 and 1.41742
