Answer
number to be added: $\dfrac{1}{36}$
factored form: $(x+\frac{1}{6})^2$
Work Step by Step
RECALL:
To complete the square of an expression in the form $x^2+bx$, $(\frac{b}{a})^2$ must be added.
The factored form of the result is $(x+\frac{b}{2})^2$.
Thus, in the given expression add $(\dfrac{\frac{1}{3}}{2})^2=(\frac{1}{6})^2=\frac{1}{36}$ to obtain:
$x^2 +\frac{1}{3}x + \frac{1}{36}$
Writing the square in factored form gives:
$x^2+\frac{1}{3}x+\frac{1}{36} = (x+\frac{1}{6})^2$
