Question 774952
{{{ n^2 + n = 77 }}}
{{{ n^2 + n + (1/2)^2 = 77 + (1/2)^2 }}}
{{{ n^2 + n + 1/4 = 77 + 1/4 }}}
{{{ ( n + 1/2 )^2 = 309/4 }}}
{{{ n + 1/2 = sqrt( 309/4 ) }}}
{{{ n = sqrt( 77.25 ) - .5 }}}
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check answer:
{{{ n^2 + n = 77 }}}
{{{ ( sqrt( 77.25 ) - .5 )^2 + sqrt( 77.25 ) - .5 = 77 }}}
{{{ 77.25 - sqrt( 77.25 ) + .25 + sqrt( 77.25 ) - .5 = 77 }}}
{{{ 77.25 + .25 - .5 = 77 }}}
{{{ 77 = 77 }}}
OK