Question 1209774
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Starting equations

    x *y =  -5     (1)
    x + y =  5     (2)


From equation (2), express  y = 5 - x and substitute it into equation (1).

    x*(5-x) = -5.


Simplify

    5x - x^2 = -5,

    x^2 - 5x - 5 = 0.


Solve quadratic equation using the quadratic formula

    {{{x[1,2]}}} = {{{(5 +- sqrt(5^2 - 4*1*(-5)))/2}}} = {{{(5 +- sqrt(45))/2}}} = {{{(5 +- 3*sqrt(5))/2}}}.


The numbers are  {{{(5+3*sqrt(3))/2}}} = 5.854101966 and  {{{(5-3*sqrt(5))/2}}} -0.854101966.    <U>ANSWER</U>


<U>CHECK</U>.  5.854101966*(-0.854101966) = -5.0000000000 with at least 10 decimals after the decimal dot.
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Solved.