What two numbers multiply together to equal 140 and when added equal 24?

Answer 1

164

Answer 2

14 and 10

Algebraically:

xy = 140

x + y = 24 yields y = 24 - x

xy = 140 replace y with 24 - x

x(24 - x) = 140 distribute x on the left side

-x2 + 24x = 140 multiply by -1 both sides

x2 - 24x = -140 complete the square by adding 122 to both sides

x2 - 24x + 122 = -140 + 144

(x - 12)2 = 4 take the square root of both sides

x - 12 = ± 2 add 12 to both sides

x = 12 ± 2

x = 12 + 2 or x = 12 - 2

x = 14 or x = 10

Thus, the numbers are 14 and 10.