Problem $12\mathrm{.}027-$ Load balancing by weight placement

The beam in the figure is weightless. A movable weight of $350lbm$ is to be attached as shown. The load $x$ is $1,800lbf.$ Determine the location $x$ of the weight so that the vertical reactions at A and $B$ are equal. $gL=32\mathrm{.}1740\frac{ft}{s^2}.($Round the final answer to four decimal places.$)$

The location $x$ of the weight is