Answer:
16 and - 2
Step-by-step explanation:
let the 2 numbers be x and y, then
xy = - 32 → (1)
x + y = 14 → (2)
Subtract y from both sides of (2)
x = 14 - y → (3)
Substitute x = 14 - y into (1)
(14 - y)y = - 32 ← distribute left side
14y - y² = - 32 ( add 32 to both sides )
14y - y² + 32 = 0 ( multiply through by - 1 )
y² - 14y - 32 = 0 ← in standard form
(y - 16)(y + 2) = 0 ← in factored form
Equate each factor to zero and solve for y
y - 16 = 0 ⇒ y = 16
y + 2 = 0 ⇒ y = - 2
Substitute these values into (3) for corresponding value of x
y = 16 → x = 14 - 16 = - 2
y = - 2 → x = 14 - (- 2) = 14 + 2 = 16
Thus the2 numbers are 16 and - 2
