What two numbers Multiply to -126 and add up to -11

AB = -126
A + B = -11

So A = -11 - B

(-11-B)B = -126
-11B - B^2 - 126

B^2 - 11B + 126 = 0

By quadratic formula we have -18 and 7. Those are both of the answers.

X*Y = -126
=> x = -126/Y

X+Y =-11
(From above) => -126/Y + Y =-11
=> multiply across by Y to get: -126 +Y^2 = -11Y+
=> Y^2 +11Y - 126 = 0

Y =( - 11 +- sqrt(121 - (-504)) ) / 2 =( -11 +- 25) / 2

Y= 7 or -18

xy = -126
x + y =-11
x = -11 - y

y(-11 - y) = -126
-11y - y^2 = -126
y^2 + 11y - 126 = 0

(x + 18)(x - 7) = 0
x = -18, 7

-18 and 7