Question

What two numbers add to get you negative 25 and multiply to get 24

Answer 1

`\begin{cases} x+y = -25 \\ xy = 24 \end{cases} \\ \\ \begin{cases} y = -25 - x \\ x(-25-x) = 24 \end{cases} \\ \\ \begin{cases} y = -25 - x \\ -25x -x^(2) = 24 \end{cases} \\ \\ \\ -x^(2) - 25x -24 = 0 \\ \\ x^(2) + 25x + 24 = 0 \\ \\ x^(2) + 24x + x +24 = 0 \\ \\ x(x+24) + (x+24) = 0 \\ \\ (x+1)(x+24) = 0 \\ \\ x+1 = 0 \ \vee \ x+24 = 0 \\ \\ x = -1 \ \vee \ x=-24 \\ \\ \\ \\ \boxed{x = -1 \ \wedge \ y = -24 \ \ \ \ \vee \ \ \ \ x = -24 \ \wedge \ y = -1}`

Answer 2

Begin by factoring 24 (the numbers that multiply together to make 24)

1&24, 2&12, 3&8, 4&6

Now, since you are looking for a negative 25, all of these combinations are negative since a negative x a negative = a positive.

The only combination that when added equals -25 is -1&-24.

and -1x-24=24

so the answer is -1&-24