Chapter 12.2, Problem 3OE

To determine

To Complete: The square $m^2+5m+\_\_\_={\left(m+\_\_\_\right)}^2$

Answer to Problem 3OE

The required answer is $m^2+5m+\frac{25}{4}={\left(m+\frac{5}{2}\right)}^2$

Explanation of Solution

Given information:

  $m^2+5m+\_\_\_={\left(m+\_\_\_\right)}^2$

Calculation:

  $\begin{array}{l}{m}^2+5m+\_\_\_={\left(m+\_\_\_\right)}^2\\ m^2+5m+{\left(\frac{5}{2}\right)}^2={\left(m+\frac{5}{2}\right)}^2\end{array}$

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

  $m^2+5m+\frac{25}{4}={\left(m+\frac{5}{2}\right)}^2$

(Simplify)