SOLUTION: What multiplies to give you -60 and adds to give you -1

Question 854758: What multiplies to give you -60 and adds to give you -1
Found 2 solutions by Fombitz, Seutip:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Let the two numbers be X and Y.
1.
2.
From eq. 2,

Substitute into eq. 1,

Use the quadratic formula,

So,
when ,

and
when ,

Answer by Seutip(231) (Show Source): You can put this solution on YOUR website!
Let a - be one of the number
b - be the second number
When given a question of this nature, you can look upon the two numbers as the factors in two polynomials that give you a quadratic when multiplied. That sounds complicated, but I mean this:

Use our friend Mr. Foil

So they give you a product of "ab" and a sum of "a + b". You are looking for exactly that, two numbers that multiply to give a product you specify and add to give the sum you specify.
If you substitute the sum, -1, and the product, -60, you get:

Since it's not a perfect trinomial we use completing the square
It's 1/4 because 3rd term = ((-1)/2)^2

Hope that helps!

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