Question

Move the values and expressions in the toolbox to solve for x by completing the square.

Response area with 6 blank spaces
x squared minus 10 x equals negative 9

x squared minus 10 x plus
Blank space 1 empty
equals negative 9 plus
Blank space 2 empty


Blank space 3 empty
equals
Blank space 4 empty



x equals
Blank space 9 empty
or x equals
Blank space 10 empty

Answer options with 24 options.

Answer 1

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:

\[
x^2 - 10x = -9
\]

\[
x^2 - 10x + \textbf{25} = -9 + \textbf{25}
\]

\[
\textbf{(x - 5)^2} = \textbf{16}
\]

\[
x = \textbf{9} \quad \text{or} \quad x = \textbf{1}
\]