Question 1065310
{{{ 2*( x - p )^2 + q = 0 }}}
{{{ 2*( x^2 - 2p*x + p^2 ) + q = 0 }}}
{{{ 2x^2 - 4p*x + 2p^2 + q = 0 }}}
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The given equation is:
{{{ 2x^2 - 5x = -12 }}}
{{{ 2x^2 - 5x + 12 = 0 }}}
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{{{ -4p = -5 }}}
{{{ p = (-5)/(-4) }}}
{{{ p = 5/4 }}} 
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{{{ 2p^2 + q = 12 }}}
{{{ 2*( 5/4 )^2 + q = 12 }}}
{{{ 2*( 25/16 ) + q = 12 }}}
{{{ q = 12 - 50/16 }}}
{{{ q = 12 - 25/8 }}}
{{{ q = 96/8 - 25/8 }}}
{{{ q = 71/8 }}}
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check:
{{{ 2*( x - p )^2 + q = 0 }}}
{{{ 2*( x - 5/4 )^2 + 71/8 = 0 }}} 
{{{ 2*( x^2 - (10/4)*x + 25/16 ) + 71/8 = 0 }}}
{{{ 2x^2 - (10/2)*x + 25/8 + 71/8 = 0 }}}
{{{ 2x^2 - 5x + 96/8 = 0 }}}
{{{ 2x^2 - 5x + 12 = 0 }}}
{{{ 2x^2 - 5x = -12 }}}
OK