Question 992363
Let {{{ x }}} = the original number of students
{{{ 1900/x - 2.5 = 1900/( x + 2 ) }}}
Multiply both sides by {{{ x*( x+2 ) }}}
{{{ 1900*( x+2 ) - 2.5*x*( x+2 ) = 1900x }}}
{{{ 1900x + 3800 - 2.5x^2 - 5x = 1900x }}}
{{{ 2.5x^2 + 5x - 3800 = 0 }}}
{{{ 25x^2 + 50x - 38000 = 0 }}}
{{{ x^2 + 2x = 1520 }}}
Complete the square
{{{ x^2 + 2x + (2/2)^2 = 1520 + (2/2)^2 }}}
{{{ x^2 + 2x + 1 = 1521 }}}
{{{ ( x + 1 )^2 = 39^2 }}}
{{{ x + 1  = 39 }}}
{{{ x = 38 }}}
38 students were in the original group
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check:
{{{ 1900/x - 2.5 = 1900/( x + 2 ) }}}
{{{ 1900/38 - 2.5 = 1900/( 38 + 2 ) }}}
{{{ 50 - 2.5 = 1900/40 }}}
{{{ 47.5 = 47.5 }}}
OK