Question 468806
Let x is the first number
Let y is the second number
A sum of two numbers is 22, then  {{{x+y=22}}}, a product of two numbers is 96, then {{{xy=96}}}
The system of the equations
{{{system(x+y=22,xy=96)}}}
From the first equation {{{y=22-x}}}
Substitute into the second equation
{{{x(22-x)=96}}}
{{{22x-x^2-96=0}}}
{{{x^2-22x+96=0}}}
{{{x = (-(-22) +- sqrt( (-22)^2-4*1*96 ))/(2*1) }}} 
{{{x = (22 +- sqrt( 100))/2 }}} 
{{{x1 = (22 +10)/2 =16}}} or {{{x2 = (22 -10)/2 =6}}}
{{{y1=22-16=6}}} or {{{y2=22-6=16}}}
The numbers 16 and 6