Question 778862
{{{ 2x^2 - 3x - 8 = 0 }}}
{{{ 2x^2 - 3x = 8 }}}
{{{ x^2 - (3/2)*x = 4 }}}
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Take 1/2 of the coefficient of the x-term,
square it, and add it to both sides
{{{ x^2 - (3/2)*x + (3/4)^2 = 4 + (3/4)^2 }}}
{{{ x^2 - (3/2)*x + 9/16 = 64/16 + 9/16  }}}
{{{ ( x -  3/4 )^2 = 73/16 }}}
Take the square root of both sides
{{{ x - 3/4 = sqrt(73)/4 }}}
{{{ x  = ( 3 + sqrt(73 )) / 4 }}}
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Now take the (-) square root of the right side
{{{ x - 3/4 = - sqrt(73 ) / 4  }}}
{{{ x = ( 3 - sqrt(73)) / 4 }}}
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check:
{{{ ( x  -  ( 3 + sqrt(73) ) / 4 ) * ( x  -  ( 3 - sqrt(73) ) / 4 ) = 0 }}}
{{{ x^2 -  (( 3 + sqrt(73) ) / 4 ) * x -  ( ( 3 - sqrt(73) ) / 4 ) *x - ( 9 - 73 )/16= 0 }}}
{{{ x^2 - (3/4)*x -  ( sqrt(73)  / 4 ) * x  - (3/4)*x +   ( sqrt(73)  / 4 ) * x - 64/16 = 0 }}}
{{{ x^2 - (3/2)*x  - 4 = 0 }}}
{{{ 2x^2 - 3x - 8 = 0 }}}
OK