What two numbers multiply to - 96 and add to 7

The numbers are x and y.

Therefore, we can suggest this system of equations:

xy=-96

x+y=7 ⇒x=7-y

solve this systeme by substitution method.

(7-y) y=-96

7y-y²=-96

y²-7y-96=0

We solve this square ecuation:

y=[7⁺₋√ (49-4 (1) (-96)) ] / 2 = (7⁺₋√433) / 2

We have two solutions:

y₁ = (7-√433) / 2 (y₁≈-6.904326 ...)

x₁=7-y₁

x₁=7 - (7-√433) / 2 = (7+√433) / 2 (x₁≈13.904326 ...)

y₂ = (7+√433) / 2 (y₂≈13.904326 ...)

x₂=7-y₂

x₂=7 - (7+√433) / 2 = (7-√433) / 2 (x₂≈-6.904326 ...)

Therefore:

The numbers are (7-√433) / 2 and (7+√433) / 2.