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To complete the square for the expression \(x^2 - x\), we follow this method:

### Step 1: Coefficient of \(x\)
The coefficient of the linear term \(x\) is \(-1\).

### Step 2: Take half of the coefficient of \(x\)
Half of \(-1\) is \(\frac{-1}{2}\).

### Step 3: Square the result
Squaring \(\frac{-1}{2}\) gives:
\[
\left(\frac{-1}{2}\right)^2 = \frac{1}{4}
\]

Thus, the number that should be added to complete the square is \(\frac{1}{4}\).

Would you like further details or have any questions?

Here are some related questions:
1. What is completing the square used for in solving quadratic equations?
2. Can completing the square be applied to any quadratic expression?
3. How do you factor a quadratic after completing the square?
4. What happens if the coefficient of \(x^2\) is not 1?
5. How can completing the square help in deriving the quadratic formula?

**Tip:** Completing the square is particularly useful when solving quadratic equations that do not factor easily.

What number should be added to complete the square of the following expression? x^2 - x.

Learn how to complete the square for the expression x^2 - x. This step-by-step guide shows the process of adding 1/4 to make the quadratic expression a perfect square. Ideal for students in Grades 8-10 studying algebra.

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