What are factors of 576 that add up to -12?

Answer 1

564

Answer 2

x + y = -12, so that y = -x - 12

xy = 576

x(-x - 12) = 576

-x2 - 12x = 576

x2 + 12x = -576

x2 + 12x + 62 = -576 + 62

(x + 6)2 = -540 this is not possible for real numbers

x + 6 = ±√-540

x = - 6 ±√-540

x = - 6 ± 6i√15

x = -6 + 6i√15 or x = -6 - 6i√15

x = -(6 - 6i√15) or x = -(6 + 6i√15)

y = - 12 - x

y = - 12 - (-6 + 6i√15) or y = -12 - (-6 - 6i√15)

y = - 12 + 6 - 6i√15 or y = -12 + 6 + 6i√15)]

y = -6 - 6i√15 or y = -6 + 6i√15

y = -(6 + 6i√15) or y = -(6 - 6i√15)

Check:

x + y = -6 + 6i√15 + -6 - 6i√15 = -12 or

x + y = -6 - 6i√15 + -6 + 6i√15 = -12

xy = [-(6 - 6i√15)][-(6 + 6i√15)] = 62 - (6i√15)2 = 36 - 540i2 = 36 + 540 = 576 or

xy = [-(6 + 6i√15)][-(6 - 6i√15)] = 62 - (6i√15)2 = 36 - 540i2 = 36 + 540 = 576