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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

1 answer

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: \[ x^2 + 6x + 9 = -5 + 9 \]

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

  2. Now, we can identify:

    • Blank space 3: 3
    • Blank space 4: 4

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

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

  2. 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 \(x = -5\)

  3. 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