To solve the equation \( x^2 - 10x = -9 \) by completing the square, we follow these steps.
Starting with the equation:
\[
x^2 - 10x = -9
\]
1. Identify the coefficient of \( x \) (which is -10), divide it by 2, and square it:
\[
\left(-\frac{10}{2}\right)^2 = (-5)^2 = 25
\]
2. Rewrite the equation by adding and subtracting this value on the left side:
\[
x^2 - 10x + 25 = -9 + 25
\]
So the filled-in blanks will look like:
- **Blank 1**: 25
- **Blank 2**: 25
- **Blank 3**: \((x - 5)^2\)
- **Blank 4**: 16
3. Now, we rewrite the equation:
\[
(x - 5)^2 = 16
\]
4. Next, we take the square root of both sides:
\[
x - 5 = \pm 4
\]
5. Finally, we solve for \( x \):
\[
x = 5 + 4 \quad \text{or} \quad x = 5 - 4
\]
\[
x = 9 \quad \text{or} \quad x = 1
\]
So, the last two blanks will be:
- **Blank 9**: 9
- **Blank 10**: 1
Putting all of this together, we fill in the blanks:
Response area with the filled blanks:
\[
x^2 - 10x = -9
\]
\[
x^2 - 10x + \textbf{25} = -9 + \textbf{25}
\]
\[
\textbf{(x - 5)^2} = \textbf{16}
\]
\[
x = \textbf{9} \quad \text{or} \quad x = \textbf{1}
\]