Question 863016
Let {{{ n }}} = the number
{{{ n^2 + n = 6 }}}
Complete the square
{{{ n^2 + n + (1/2)^2 = 6 + (1/2)^2 }}}
{{{ n^2 + n + 1/4 = 6 + 1/4 }}}
{{{ ( n + 1/2 )^2 = 25/4 }}}
{{{ ( n + 1/2 )^2 = ( 5/2 )^2 }}}
Take the square root of both sides
{{{ n + 1/2 = 5/2 }}}
{{{ n = 4/2 }}}
{{{ n = 2 }}}
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check answer:
{{{ 2^2 + 2  = 6 }}}
{{{ 4 + 2 = 6 }}}
{{{ 6 = 6 }}}
OK
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A negative number also satisfies the equation
{{{ n + 1/2 = -(5/2) }}}
{{{ n = -(6/2) }}}
{{{ n = -3 }}}
and
{{{ (-3)^2 + (-3) = 6 }}}
{{{ 9 - 3 = 6 }}}
{{{ 6 = 6 }}}
OK