Fill in the steps to complete the square:

Question

x2 +12x − 14 = 0

x2 + 12x = 14

x2 +12x +
Response area = 14+
Response area

We factor and simplify to get:

(x+6)2 =
Response area

At this point, we need to Response area

After that is done, we will have:

Response area =
Response area

We get isolate the variable by:

Response area

Final answers are:

Response area





The option "square both sides of the equation. " (17 of 24) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.

Answer 1

Let's fill in the steps to complete the square for the equation \( x^2 + 12x - 14 = 0 \).

1. Start with the equation: \[ x^2 + 12x - 14 = 0 \]

2. Move the constant term to the other side: \[ x^2 + 12x = 14 \]

3. Complete the square by adding and subtracting the square of half the coefficient of \(x\): \[ x^2 + 12x + 36 = 14 + 36 \]

4. The \( 36 \) is obtained by taking half of \( 12 \) (which is \( 6 \)) and squaring it (\( 6^2 = 36 \)).

5. Now we simplify: \[ (x + 6)^2 = 50 \]

6. At this point, we need to take the square root of both sides: \[ x + 6 = \pm \sqrt{50} \]

7. This can be simplified further: \[ x + 6 = \pm 5\sqrt{2} \]

8. Now we isolate the variable by subtracting \( 6 \) from both sides: \[ x = -6 \pm 5\sqrt{2} \]

Final answers are: \[ x = -6 + 5\sqrt{2} \quad \text{and} \quad x = -6 - 5\sqrt{2} \]

So, let's summarize the filled areas:

• x² + 12x + 36 = 14 + 36
• (x + 6)² = 50
• Take the square root of both sides
• x = -6 ± 5√2

Answer 2

u forgot: After that is done, we will have:

Response area =
Response area

We get isolate the variable by:

Response area

Final answers are:

Answer 3

I apologize for missing those specifics. Let’s fill in the additional response areas as requested:

1. Start with the equation: \[ x^2 + 12x - 14 = 0 \]

2. Move the constant term to the other side: \[ x^2 + 12x = 14 \]

3. Complete the square by adding and subtracting the square of half the coefficient of \(x\): \[ x^2 + 12x + 36 = 14 + 36 \]

4. We now have: \[ (x + 6)^2 = 50 \]

After that is done, we will have: \[ (x + 6)^2 = 50 \]

We get isolate the variable by: \[ x + 6 = \pm \sqrt{50} \]

Final answers are: \[ x = -6 + 5\sqrt{2} \quad \text{and} \quad x = -6 - 5\sqrt{2} \]

Here's the complete sequence:

• x² + 12x + 36 = 14 + 36
• (x + 6)² = 50
• After that is done, we will have: (x + 6)² = 50
• We get isolate the variable by: x + 6 = ±√50
• Final answers are: x = -6 + 5√2 and x = -6 - 5√2.

Answer 4

We get isolate the variable by:

Response area

Final answers are:

Answer 5

I see you're looking for a more direct response for those specific areas. Here’s the requested completion:

We get isolate the variable by: \[ x = -6 \pm \sqrt{50} \]

Final answers are: \[ x = -6 + 5\sqrt{2} \quad \text{and} \quad x = -6 - 5\sqrt{2} \]

So here’s the complete response including those lines:

1. Start with the equation: \[ x^2 + 12x - 14 = 0 \]

2. Move the constant term to the other side: \[ x^2 + 12x = 14 \]

3. Complete the square by adding and subtracting the square of half the coefficient of \(x\): \[ x^2 + 12x + 36 = 14 + 36 \]

4. Now we have: \[ (x + 6)^2 = 50 \]

After that is done, we will have: \[ (x + 6)^2 = 50 \]

We get isolate the variable by: \[ x = -6 \pm \sqrt{50} \]

Final answers are: \[ x = -6 + 5\sqrt{2} \quad \text{and} \quad x = -6 - 5\sqrt{2} \]

If you need any changes or further assistance, feel free to ask!