Chapter 12.2, Problem 4OE

To determine

To Complete: The square $r^2-11r+\_\_\_={\left(r-\_\_\_\right)}^2$ .

Answer to Problem 4OE

The required answer is $r^2-11r+\frac{121}{4}={\left(r-\frac{11}{2}\right)}^2$ .

Explanation of Solution

Given information:

  $r^2-11r+\_\_\_={\left(r-\_\_\_\right)}^2$

Calculation:

  $\begin{array}{l}{r}^2-11r+\_\_\_={\left(r-\_\_\_\right)}^2\\ r^2-11r+{\left(\frac{11}{2}\right)}^2={\left(r-\frac{11}{2}\right)}^2\end{array}$

(Taking the constant term as square of half the coefficient of r)

  $r^2-11r+\frac{121}{4}={\left(r-\frac{11}{2}\right)}^2$

(Simplify)