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

Question

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:

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

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

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

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