Question 517039
{{{ n + 21*(1/n) = -10 }}}
Multiply both sides by {{{n}}}
{{{ n^2 + 21 = -10n }}}
{{{ n^2 + 10n = -21 }}}
Complete the square
{{{ n^2 + 10n + (10/2)^2 = -21 + (10/2)^2 }}}
{{{ n^2 + 10n + 25 = -21 + 25 }}}
{{{ ( n + 5 )^2 = 4 }}}
Take the square root of both sides
{{{ n + 5 = 2 }}}
{{{ n = -3 }}}
and also
{{{ n + 5 = -2 }}}
{{{ n = -7 }}}
check answers:
{{{ n + 21*(1/n) = -10 }}}
{{{ -3 + 21*(1/(-3)) = -10 }}}
{{{ -3 - 7 = -10 }}}
{{{ -10 = -10 }}}
OK
{{{ -7 + 21*(1/(-7)) = -10 }}}
{{{ -7 - 3 = -10 }}}
{{{ -10 = -10 }}}