Question

What 2 numbers add to get -9 and multiply to get -30?​

Answer 1

`y_(1)=-(9)/(2)-(√(201))/(2)` or
`y_(2)=-(9)/(2)+(√(201))/(2)`

`x_(1)=-(9)/(2)-(√(201))/(2)` or
`x_(2)=-(9)/(2)+(√(201))/(2)`

Explanation:

Let be x the first number and y the second number.

So we have:

`x+y=-9` (1)

`x*y=-30` (2)

Solve x from equation 1 and put it into equation 2

`x=-9-y`

`(-9-y)*y=-30`

`-9y-y^(2)=-30`

`y^(2)+9y-30=0`

Solving this quadratic equation and put it on the equation (1) the solutions will be:

`y_(1)=-(9)/(2)-(√(201))/(2)` or
`y_(2)=-(9)/(2)+(√(201))/(2)`

`x_(1)=-(9)/(2)-(√(201))/(2)` or
`x_(2)=-(9)/(2)+(√(201))/(2)`

I hope it helps you!