Question

Which two numbers add up to 5 and multiply to -45 ?

Answer 1

we have x+y=5
xy=-45
solve
x+y=5
subtract x from both sides
y=-x+5
subsiute -x+5 for y in second equaiton
x(-x+5)=-45
-x^2+5x=-45
add 2x^2-5x to both sides
0=x^2-5x-45
use quadratic equation which is
if you have 0=ax^2+bx+c then x=
`\frac{-b+ \sqrt{b^(2)-4ac} }{2a}` or
`\frac{-b- \sqrt{b^(2)-4ac} }{2a}`
sbsitute
1x^2-5x-45
a=1
b=-5
c=-45
subsitute

`\frac{-(-5)+ \sqrt{-5^(2)-4(1)(-45)} }{2(1)}`

`(5+ √(25-(-180)) )/(2)`

`(5+ √(25+180) )/(2)`

`(5+ √(205) )/(2)`

`image` or
`\frac{5- \sqrt{} }{2}` or aprox x=-4.65891 or 9.65891, so the 2 numbers would be those answers for x