What two numbers add to equal -16 & multiply to equal-36

Answer 1

Here's what we know:

x + y = -16 (two numbers added together equal -16)

xy = -36 (when multiplied together, they're -36)

Let's isolate a variable in the first equation so we can substitute:

x = -y - 16

And now place it in the other equation:

y(-y - 16) = -36

Distribute:

-y² - 16y = -36

Okay, we can see where this is going, into a quadratic:

-y² - 16y + 36 = 0

Multiply by -1 to make it easier to read for us:

y² + 16y - 36 = 0

Now to factor where n + m = 16, and nm = -36. ..... Did we just hit Deja vu? No, almost. the 16 here is positive:

(y + 18)(y - 2) = 0

y + 18 = 0, and y - 2 = 0

y = -18, 2

So our two numbers are -18 and 2.