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

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

May 1, 2020

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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 $$2\sqrt{11} - 3$$