Chapter 8 - Section 8.1 - The Square Root Property and Completing the Square - Exercise Set - Page 593: 27

$(x+\dfrac{7}{2})^2$

Given: $x^2+7x$ We need to add $(\dfrac{7}{2})^2$ to complete the square. Thus, $x^2+7x+(\dfrac{7}{2})^2=x^2+7x+\dfrac{49}{4}$ Apply sum of polynomial formula. or, $x^2+(\dfrac{7}{2})^2+(2)(x)(\dfrac{7}{2})=(x+\dfrac{7}{2})^2$