6. For what value of $x$ does the expression $x^{2}-600 x+369$ take its minimum value?
SOLUTION
300

Complete the square on $x^{2}-600 x+369$ to obtain $(x-300)^{2}-300^{2}+369$.
The minimum value of this expression will occur when $(x-300)^{2}=0$. This is when $x=300$.