SOLUTION: Number that multiplies to -44 but adds to -1

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Question 1210275: Number that multiplies to -44 but adds to -1
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!
Numbers that multiply to -44 but add to -1.

Trial and error, or any other method, shows that there are not any two rational numbers that satisfy the conditions. So...

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Solve using the quadratic formula.



ANSWER: the two numbers are and


Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.

Here is another solution. 

Since the sum of the numbers is -1, it means that the numbers are equally remoted from -0.5,
so we can write

    a = -0.5 + x,

    b = -0.5 - x.


Thus a + b = -1 is provided, and we should satisfy the other condition

    a*b = -44.


It gives

    (-0.5+x)*(-0.5-x) = -44,

     -  = -44,

    0.025 + 44 = 

     = 44.25

    x = .


Thus,  the numbers are  a =  = ,  b =  = .

Solved.

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I posted this solution to surprise you that such simple problem may have two different approaches.
My other goal was to show you a solution which has a geometric meaning - not only a calculation exercise.



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