Answer
$(x-\dfrac{9}{8})^2$
Work Step by Step
Given: $x^2-\dfrac{9}{4}x$
We need to add $(\dfrac{-9}{8})^2$ to complete the square.
Thus,
$x^2-\dfrac{9}{4}x+(\dfrac{-9}{8})^2=x^2-\dfrac{9}{4}x+\dfrac{81}{64}$
Apply difference of polynomial formula.
or, $x^2+(\dfrac{9}{8})^2-(2)(x)(\dfrac{9}{8})=(x-\dfrac{9}{8})^2$
