Answer
$(x+\dfrac{2}{3})^2$
Work Step by Step
Given: $x^2+\dfrac{4}{3}x$
We need to add $(\dfrac{2}{3})^2$ to complete the square.
Thus,
$x^2+\dfrac{4}{3}x+(\dfrac{2}{3})^2=x^2+\dfrac{4}{3}x+\dfrac{4}{9}$
Apply sum of polynomial formula.
or, $x^2+(\dfrac{2}{3})^2+(2)(x)(\dfrac{2}{3})=(x+\dfrac{2}{3})^2$
