Question 854758
Let the two numbers be X and Y.
1.{{{X*Y=-60}}}
2.{{{X+Y=-1}}}
From eq. 2,
{{{X=-1-Y=-(1+Y)}}}
Substitute into eq. 1,
{{{-(1+Y)Y=-60}}}
{{{Y+Y^2=60}}}
{{{Y^2+Y-60=0}}}
Use the quadratic formula,
{{{Y = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{Y = (-1 +- sqrt( 1^2-4*1*(-60) ))/(2*1) }}}
{{{Y = (-1 +- sqrt( 1+240 ))/(2) }}}
{{{Y = (-1 +- sqrt( 241 ))/(2) }}}
So, 
when {{{Y = (-1 + sqrt( 241 ))/(2) }}},
{{{X=-1- (-1 + sqrt( 241 ))/(2) }}}
{{{X=-1+1/2-sqrt(241)/2}}}
{{{X=-1/2-sqrt(241)/2}}}
and
when {{{Y = (-1 - sqrt( 241 ))/(2) }}},
{{{X=-1- (-1 - sqrt( 241 ))/(2) }}}
{{{X=-1+1/2+sqrt(241)/2}}}
{{{X=-1/2+sqrt(241)/2}}}