What two numbers mutiply into -35, add into -6

Some people may be able to figure it out in a few seconds, but we can use some variables to solve it. Let's call them  "a" and "b".

 

We know that ab = -35, and a + b = -6

We can express one variable in terms of another, to reduce into a one-variable equation which is easy to solve!

 

We could write a = -6 -b, or b = -6 - a. Let's go with the first one.

 

(-6 - b)b = -35

-6b - b² = -35

 

Wow, it's a quadratic (has an exponent of 2 on the variable) :D 

 

We can rearrange this into the standard form for quadratic equations (ax² + bx + c = 0).

 

-b² - 6b + 35 = 0. 

Using any method of solving quadratic equations, we get some really weird numbers for a and b that still fit:

 

\(-3 - 2\sqrt{11} \) and also \(2\sqrt{11} - 3\)

So, well... there's your answer! :D