What two numbers multiplied equals -6 and added equals 15?

Answer 1

9

Answer 2

Lets call the two numbers x and y. We know that xy = -6 and that x + y = -15.

If we solve the second equation for y, we get y = 15-x. Plug 15-x into the first equation (xy = -6) for y: x(15-x) = -6

Distribute:

15x-x2=-6

Add 6 to both sides:

-x2+15x+6=0

You don't have to, but we'll multiply both sides by -1 so that x2 is positive.

x2-15x-6=0

Use the quadratic formula:

x = (-(15)±√((-15)2-4(-1)(-6)))/(2(1))

x = (15±√(249))/2

Because of the plus or minus, both numbers are represented, so the two numbers are:

(1/2)(15+√249) and (1/2)(15-√249)