SOLUTION: What two numbers add to -5 and multiply to 6

Although the solution can be discovered by 5-10 seconds of observation, here are the steps needed to solve it procedurally (so you'll know how to solve problems when the solution is not so obvious):



x + y = -5  (1)  —> y = -5 - x

xy = 6   (2)



Substitute for y from (1) in (2):  

x(-5-x) = 6

    





 and 



x=-3 ==> y = -5 - (-3) = -2

x=-2 ==> y = -5 - (-2) = -3   (so this case is just the x & y values swapped, we can accept either one since x and y have no special meaning here)



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Ans: The numbers satisfying the given criteria are  and 

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Check:  -2 - 3 = -5  (ok)

     and  (-2)*(-3) = 6  (ok)

 

All you need to do is determine the factors of 6. These are 6 and 1, or 3 and 2. 

Now, as the product is POSITIVE (+ 6), the factors are either going to have 2 negatives or 2 positives. Based on the fact that the sum is negative (- 5), 

we either get - 6 and - 1, or - 3 and - 2. As - 6 and - 1 DON'T sum to - 5, then they MUST be: 

That's all!!