Question

What two numbers add up to -19 and have a product of 70

Answer 1

x + y = -19
xy = 70

x + y = -19
x - x + y = -x - 19
y = -x - 19

xy = 70
x(-x - 19) = 70
x(-x) + x(-19) = 70
-x² - 19x = 70
-x² - 19x - 70 = 0
-1(x²) - 1(19x) - 1(70) = 0
-1(x² + 19x + 70) = 0
-1 -1
x² + 19x + 70 = 0
x² + 14x + 5x + 70 = 0
x(x) + x(14) + 5(x) + 5(14) = 0
x(x + 14) + 5(x + 14) = 0
(x + 5)(x + 14) = 0
x + 5 = 0 or x + 14 = 0
- 5 - 5 - 14 - 14
x = -5 or x = -14

x + y = -19
-5 + y = -19
+ 5 + 5
y = -14
(x, y) = (-5, -14)

or

x + y = -19
-14 + y = -19
+ 14 + 14
y = -5
(x, y) = (-14, -5)

The two numbers that add up to -19 and multiply to 70 are -14 and -5.

Answer 2

-5+-14 would equal -19 and multiply to 70