\(\text{Square A and Square B are both $2009$ by $2009$ squares. Square A has both its length and width increased by an amount $x$, while Square B has its length and width decreased by the same amount $x$. What is the minimum value of $x$ such that the difference in area between the two new squares is at least as great as the area of a $2009$ by $2009$ square? }\)
+6248 reposted for readability
\(\text{Square A and Square B are both $2009$ by $2009$ squares.$\\$ Square A has both its length and width increased by an amount $x,\\$ while Square B has its length and width decreased by the same amount $x.\\~\\$ What is the minimum value of $x$ such that the difference in area between$\\$ the two new squares is at least as great as the area of a $2009$ by $2009$ square? }\)
