What number adds together to give -8 and multiple together to give 6?

Answer 1

Let's x be one of the numbers, and y the other number. So,

x + y = -8

xy = 6

y = -x - 8

x(-x -8) = 6

-x^2 - 8x = 6 multiply by -1 both sides

x^2 + 8x = -6 solve for x by completing the square;

x^2 + 8x + 16 = -6 + 16

(x + 4)^2 = 10

x + 4 = square root of 10

x = -4 + square root of 10 or x = -4 - square root of 10

if we continue to solve the system of the equations, we can find the same value for y.

Thus the numbers are -4 + square root of 10 and -4 - square root of 10.

Check:

(-4 + square root of 10) + (-4 - square root of 10)

= -4 + square root of 10 - 4 - square root of 10

= -8

(-4 + square root of 10)(-4 - square root of 10)

= (-4)^2 - (square root of 10)^2

= 16 - 10

= 6