Question 1210275
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Here is another solution.


<pre>
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,

    {{{0.5^2}}} - {{{x^2}}} = -44,

    0.025 + 44 = {{{x^2}}}

    {{{x^2}}} = 44.25

    x = {{{sqrt(44.25)}}}.


Thus,  the numbers are  a = {{{-0.5 + sqrt(44.25)}}} = {{{(-1 + sqrt(177))/2}}},  b = {{{-0.5 - sqrt(44.25)}}} = {{{(-1 - sqrt(177))/2}}}.
</pre>

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.