Question 1135200
Let {{{ n }}} = the negative real number
{{{ ( n + 21 )^2 = 144 }}}
{{{ n^2 + 42n + 441 = 144 }}}
{{{ n^2 + 42n = -297 }}}
complete the square
{{{ n^2 + 42n + (42/2)^2 = -297 + (42/2)^2 }}}
{{{ n^2 + 42n + 441 = 144 }}} ( what I started with )
{{{ ( n + 21 )^2 = 12^2 }}}
{{{ n + 21 = 12 }}}
{{{ n = -9 }}}
and also:
{{{ ( n + 21 )^2 = (-12)^2 }}}
{{{ n + 21 = -12 }}}
{{{ n = -33 }}}
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check the answers:
{{{ ( n + 21 )^2 = 144 }}}
{{{ ( -9 + 21 )^2 = 12^2 }}}
{{{ 12^2 = 12^2 }}}
OK
{{{ ( -33 + 21 )^2 = 12^2 }}}
{{{ (-12)^2 = 12^2 }}}
{{{ 144 = 144 }}}
OK