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What number adds together to give -8 and multiple together to give 6?
Wiki User
∙ 15y ago
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
Wiki User
∙ 15y ago
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