Find the number that should be added to the expression to make it a perfect square. $$ k^{2}-5 k $$

Question

UpStudy AI · Accepted Answer

To make the expression $$ k^{2} - 5k $$ a perfect square, we can complete the square. Here's how you can do it:

1. **Start with the given expression:**
   $$
   k^2 - 5k
   $$

2. **Identify the coefficient of $$ k $$:**
   The coefficient of $$ k $$ is $$-5$$.

3. **Calculate half of the coefficient and square it:**
   $$
   \left(\frac{-5}{2}\right)^2 = \frac{25}{4}
   $$

4. **Add this square to the original expression to complete the square:**
   $$
   k^2 - 5k + \frac{25}{4} = \left(k - \frac{5}{2}\right)^2
   $$

So, the number you need to add to $$ k^2 - 5k $$ to make it a perfect square is:

$$
\boxed{\dfrac{25}{4}}
$$
You need to add $$ \frac{25}{4} $$ to $$ k^{2} - 5k $$ to make it a perfect square.

Find the number that should be added to the expression to make it a perfect square. \( k^{2}-5 k \)