Question

To complete the square of$x^2+5x,$add$\_\_\_\_\_\_\_\_\_\_$

Short answer

To complete the square of$x^2+5x,$add$\frac{25}{4}$

Step-by-step solution

Step 1. Aim of the problem

In this problem, we need to find the term to complete the square of$x^2+5x$

Step 2. Concept

Follow the below steps to find the missing term:

a. Divide the coefficient of $x$by role="math" $2.$

b. Square the answer obtained in Step a.

Step 3. Finding the missing term

To find the missing term, first divide the coefficeint of $x$by role="math" $2.$

The coefficient of $x$is $5.$Hence divide $5$by $2$.

Now take the square of $\frac{5}{2}$.

We have,

${\frac{5}{2}}^2=\frac{25}{4}$

Therefore, we must add the term $\frac{25}{4}$to complete the square of$x^2+5x.$