SOLUTION: Find two numbers whose sum is -5 and whose product is -24.

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Question 1134697: Find two numbers whose sum is -5 and whose product is -24.
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Try factors of -24.

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
The standard way is to write a quadratic equation


    x*(-5 - x) = -24,


where x is one of the two numbers and -5 - x is the other number.


Then you transform the equation into the simpler equivalent form


    x*(x + 5) = 24,

    x^2 + 5x - 24 = 0.


At this point, you can find the solution by using the quadratic formula or by factoring


    (x+8)*(x-3) = 0.


The numbers are -8 and 3.      ANSWER


There is much simpler way to solve the problem MENTALLY without using equations. 


In such problems, as a rule, the solutions are integer numbers.


So, you try guessing the factors of the number -24 that sum up to -5.


You will try  24 = 12*2 = 6*4 = 8*3  and very fast you will find the ANSWER:


    the numbers are  -8  and  3,  exactly the same as in the solution above.



After solving one - two - three such problems,  you will be able to guess the answer  MENTALLY  and  MOMENTARILY.

demonstrating  a good style  solving such problems.


But in that cases when such an approach does not work,  you must apply the full scale solution using quadratic equations.