What value can you add in the blank in the expression x^2 
 + 6x + 5 + __ to complete the square?

To complete the square in the expression \( x^2 + 6x + 5 \), you need to focus on the quadratic and linear terms first: \( x^2 + 6x \).

1. Take the coefficient of \( x \), which is 6, divide it by 2, and then square the result:
   \[
   \left(\frac{6}{2}\right)^2 = 3^2 = 9
   \]

2. The value that should be added to the expression to complete the square is 9.

Now the expression can be written as:
\[
x^2 + 6x + 9
\]
which factors as \( (x + 3)^2 \).

So, you would add **9** in the blank to complete the square.

Would you like more details or have any other questions?

Here are 5 related questions:
1. How can you complete the square for a different quadratic expression, like \( x^2 + 4x + 1 \)?
2. What is the completed square form of \( x^2 - 8x + 12 \)?
3. How can completing the square help in solving quadratic equations?
4. How is completing the square used in deriving the quadratic formula?
5. What if the leading coefficient is not 1? How do you complete the square in that case?

**Tip**: Completing the square is especially useful when solving quadratic equations or rewriting them in vertex form.

What value can you add in the blank in the expression x^2 + 6x + 5 + __ to complete the square?

Learn how to complete the square for the quadratic expression x^2 + 6x + 5. This detailed step-by-step guide explains the key concepts, including the formula for completing the square. Perfect for students in Grades 9-10 learning algebra.

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