Chapter 12.2, Problem 1OE

To determine

To Complete: The square $z^2+18z+\_\_\_={\left(z+\_\_\_\right)}^2$ .

Answer to Problem 1OE

The required answer is $z^2+18z+81={\left(z+9\right)}^2$ .

Explanation of Solution

Given information:

  $z^2+18z+\_\_\_={\left(z+\_\_\_\right)}^2$

Calculation:

  $\begin{array}{l}{z}^2+18z+\_\_\_={\left(z+\_\_\_\right)}^2\\ z^2+18z+{\left(\frac{18}{2}\right)}^2={\left(z+\frac{18}{2}\right)}^2\end{array}$

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

  $z^2+18z+81={\left(z+9\right)}^2$

(Simplify)