Question 850953
{{{ x^2 + 11x + 30 = 0 }}}
( it is set to zero to finds the roots )
Subtract {{{ 30 }}} from both sides
{{{ x^2 + 11x = -30 }}}
---------------------
To complete the square, take 1/2 of 
the coefficient of the {{{ x }}} term,
square it, and add it to both sides
------------------------------
{{{ x^2 + 11x + ( 11/2 )^2 = -30 + (11/2 )^2 }}}
{{{ x^2 + 11x + 121/4  = -120/4 + 121/4 }}}
{{{ x^2 + 11x + 121/4  = 1/4 }}} 
{{{ ( x + 11/2 )^2 = (1/2)^2 }}}
Take the square root of both sides
{{{ x + 11/2 = 1/2 }}}
{{{ x = -11/2 + 1/2 }}}
{{{ x = -5 }}}
and, also
{{{ x = -11/2 - 1/2 }}}
{{{ x = -6 }}}
-------------
{{{ x + 5 = 0 }}}
{{{ x + 6 = 0 }}}
{{{ ( x + 5 )*( x + 6 ) = 0
{{{ x^2 + 11x + 30 = 0 }}}
OK
the solutions are
{{{ x = -5 }}}
{{{ x = -6 }}}