Question 1058124
{{{ 230 = C(x) }}}
{{{ 230 = x^2  - 40x + 530 }}}
{{{ x^2 - 40x = -300 }}}
Complete the square
{{{ x^2 - 40x + (40/2)^2 = -300 + (40/2)^2 }}}
{{{ x^2 - 40x + 400  = -300 + 400 }}}
{{{ ( x - 20 )^2 = 100 }}}
Take the square root of both sides
{{{ x - 20 = 10 }}}
{{{ x = 30 }}}
and, taking the negative square root of {{{ 100 }}},
{{{ x - 20 = -10 }}}
{{{ x = 10 }}}
This says either {{{ x = 10 }}} or {{{ x = 30 }}} works
--------------------
Here's the plot:
{{{ graph( 400, 400, -10, 50, -100, 500, x^2 - 40x + 300 ) }}}