Question 712158
Let the positive number = {{{ n }}}
It's square is {{{ n^2 }}}
given:
{{{ n + n^2 = 240 }}}
Subtract {{{ 240 }}} from both sides
{{{ n^2 + n - 240 = 0 }}}
Note that {{{ 15*16 = 240 }}}, so
{{{ ( n + 16 )*( n - 15 ) = 0 }}}
The solutions are:
{{{ n = -16 }}} and
{{{ n = 15 }}}
The number has to be positive, so
{{{ n = 15 }}}
check:
{{{ n + n^2 = 240 }}}
{{{ 15 + 15^2 = 240 }}}
{{{ 15 + 225 = 240 }}}
{{{ 240 = 240 }}}
OK