Question

What are two numbers multiplied together to get 15 but add to be 12?

Answer 1

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=
`( 12+/- √(144-60) )/(2)`
x=
`( 12+/- √(84) )/(2)`
x=
`( 12+/- 2√(21) )/(2)`
x=6+/-
`√(21)`
x=6+
`√(21)` or 6-
`√(21)` or aprox
x=10.5826 or 1.41742
the numbers are 10.5826 and 1.41742