Question 1030050
I can complete the square
{{{ x^2 + 5x + 6 = 0 }}}
{{{ x^2 + 5x + (5/2)^2 = -6 + (5/2)^2 }}}
{{{ x^2 + 5x + 25/4 = -24/4 + 25/4 }}}
{{{ x^2 + 5x + 25/4 = 1/4 }}}
{{{ ( x + 5/2 )^2 = (1/2)^2 }}}
{{{ x + 5/2 = 1/2 }}}
{{{ x = -5/2 + 1/2 }}}
{{{ x = -2 }}}
and, also:
{{{ x + 5/2 = -1/2 }}}
{{{ x = -5/2 - 1/2 }}}
{{{ x = -3 }}}
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check:
{{{ ( x + 2 )*( x + 3 ) = x^2 + 5x + 6 }}}
{{{ x^2 + 5x + 6 = x^2 + 5x + 6 }}}
OK
Here's the plot:

{{{ graph( 400, 400, -10, 2, -2, 10, x^2 + 5x + 6 ) }}}