Question

Drag numbers to the lines to solve x squared plus 6 x plus 5 equals 0 by completing the square.

Response area with 8 blank spaces
x squared plus 6 x plus 5 equals 0
x squared plus 6 x plus
Blank space 1 empty
equals negative 5 plus
Blank space 2 empty

left-parenthesis x plus
Blank space 3 empty
right-parenthesis squared equals
Blank space 4 empty

x plus
Blank space 5 empty
equals plus or minus
Blank space 6 empty

x equals
Blank space 7 empty

or

x equals
Blank space 8 empty

Answer options with 19 options.
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9

Answer 1

To solve the equation \(x^2 + 6x + 5 = 0\) by completing the square, let's fill in the blanks step by step:

1. Start with the equation:
\[
x^2 + 6x + 5 = 0
\]

2. Rearrange it:
\[
x^2 + 6x + \_ = -5 + \_
\]
Here, you need to complete the square.

3. To complete the square, you take half of the coefficient of \(x\), which is \(6\), and square it:
- Half of 6 is \(3\), and squaring it gives \(9\).

4. Now, fill in the blanks:
- Blank space 1: **9**
- Blank space 2: **9**

The equation now looks like:
\[
x^2 + 6x + 9 = -5 + 9
\]

5. This simplifies to:
\[
(x + 3)^2 = 4
\]

6. Now, we can identify:
- Blank space 3: **3**
- Blank space 4: **4**

The equation is now:
\[
(x + 3)^2 = 4
\]

7. Next, take the square root of both sides:
\[
x + 3 = \pm 2
\]

8. The next steps involve isolating \(x\):
\[
x = -3 \pm 2
\]

This gives us two separate equations:
- \(x = -3 + 2\) which is \(x = -1\)
- \(x = -3 - 2\) which is \(x = -5\)

9. Finally, we can fill in:
- Blank space 5: **3**
- Blank space 6: **2**
- Blank space 7: **-1**
- Blank space 8: **-5**

In summary, here are all the filled in values:

- Blank space 1: **9**
- Blank space 2: **9**
- Blank space 3: **3**
- Blank space 4: **4**
- Blank space 5: **3**
- Blank space 6: **2**
- Blank space 7: **-1**
- Blank space 8: **-5**