what two numbers added together make 49 but when
multiplied equal a negative 100
x + y = 49 xy = -100
y = 49 - x x(49 - x) = -100
x(49 - x) = -100
49x - x^2 = -100
-1 * (49x - x^2) = -100 * -1
-49x + x^2 = 100
x^2 - 49x = 100 1/2 of 49 is 24.5
Complete the square
x^2 - 49x + 24.5^2 = 100 + 24.5^2
(x - 24.5)^2 = 100 + 600.25 = 700.25
Take the square root of both sides
x - 24.5 = ±26.462237 This has been rounded, so multiplication that
use these values will be slightly off
x = 26.462237 + 24.5 = 50.962237
x = -26.462237 + 24.5 = -1.962237
50.962237 + (-1.962237) = 49
50.962237 - 1.962237 = 49
50.962237 * (- 1.962237) = -99.999987
The two numbers are 50.962237 and -1.962237