What two numbers multiply to -12 and add to -8?

Answer 1

-20

Answer 2

(Important note: I will work to 4 decimal places as this seems a reasonable level of accuracy. If you wish a more precise answer then simply follow the steps below and round to more decimal places.)

The two numbers are -9.2915 and 1.2915 (answer given to 4 decimal places only)

1. x * y = -12

2. x + y = -8

We can rewrite 2. as x = -y - 8

We can substitute x = -y - 8 into 1. to give:

3. (-y - 8) * y = -12

Therefore -y2 - 8y = -12

-y2 -8y + 12 = 0

This is a quadratic equation and can be solved using the quadratic formula:

For Ax2 + Bx + C = 0 then

x = (-b plus or minus (b2 - 4ac)1/2) / 2a

Substituting in our values for = -y2 -8y + 12 = 0 gives us:

y = (8 + or - (-82 - (4 * -1 * 12))1/2) / (2 * -1)

y = (8 + or - 1121/2) / -2

y = -9.2915 (to 4 decimal places only) & 1.2915 (to 4 decimal places only)

Therefore the two numbers are -9.2915 & 1.2915 (and x or y could be either) the proof of which is below for additional information only.

Substituting the values y = -9.2915 & y = 1.2915 into 2. gives:

For y = -9.2915 then

x + -9.2915 = -8

x = -8 + 9.2915

x = 1.2915

For y = 1.2915 then

x + 1.2915 = -8

x = -8 - 1.2915

x = -9.2915