Chapter 8 - Section 8.1 - The Square Root Property and Completing the Square - Exercise Set - Page 593: 34

$(x-\dfrac{9}{10})^2$

Given: $x^2-\dfrac{9}{5}x$ We need to add $(\dfrac{-9}{10})^2$ to complete the square. Thus, $x^2-\dfrac{9}{5}x+(\dfrac{-9}{10})^2=x^2-\dfrac{9}{5}x+\dfrac{81}{100}$ Apply difference of polynomial formula. or, $x^2-2(x)(\dfrac{9}{10})+(\dfrac{9}{10})^2=(x-\dfrac{9}{10})^2$