Chapter 8 - Section 8.1 - The Square Root Property and Completing the Square - Exercise Set - Page 593: 28

$(x+\dfrac{9}{2})^2$

Given: $x^2+9x$ We need to add $(\dfrac{9}{2})^2$ to complete the square. Thus, $x^2+9x+(\dfrac{9}{2})^2=x^2+9x+\dfrac{81}{4}$ Apply sum of polynomial formula. or, $x^2+(\dfrac{9}{2})^2+(2)(x)(\dfrac{9}{2})=(x+\dfrac{9}{2})^2$