Question 904912
{{{ 12x^2 - 5x - 7 = 0 }}}
{{{ 12x^2 - 5x = 7 }}}
{{{ x^2 - (5/12)*x = 7/12 }}}
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Take 1/2 the coefficient of the x term,
square it, and add it to both sides
{{{ x^2 - (5/12)*x + (5/24)^2 = 7/12 + (5/24)^2 }}}
{{{ x^2 - (5/12)*x + 25/576 = 336/576 + 25/576 }}} 
{{{ x^2 - (5/12)*x + 25/576 = 361/576 }}} 
{{{ ( x - 5/24 )^2 = ( 19/24 )^2 }}}
Take the square root of both sides
{{{ x - 5/24 = 19/24 }}}
{{{ x = 24/24 }}}
{{{ x = 1 }}}
and
{{{ x = 5/24 = -19/24 }}}
{{{ x = -14/24 }}}
{{{ x = -7/12 }}}
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check:
{{{ ( x - 1 )* ( x + 7/12 ) }}}
{{{ x^2 - x + (7/12)*x - 7/12 = 0 }}}
{{{ x^2 - (5/12)*x - 7/12 = 0 }}}
{{{ 12x^2 - 5x - 7 = 0 }}}
OK