Question

Fill in the steps to complete the square:

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

Answer 1

Answer more simply

Answer 2

We get isolate the variable by?

Answer 3

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

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

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

3. To complete the square, we take half of the coefficient of \( x \) (which is 12), square it, and add it to both sides. Half of 12 is 6, and squaring it gives us 36:
\[
x^2 + 12x + 36 = 14 + 36
\]

4. Now we can rewrite the left side as a squared binomial:
\[
(x + 6)^2 = 50
\]

5. Now take the square root of both sides:
\[
x + 6 = \pm \sqrt{50}
\]

6. This simplifies to:
\[
x + 6 = \pm 5\sqrt{2}
\]

7. Isolate the variable \( x \):
\[
x = -6 \pm 5\sqrt{2}
\]

The final answers are:
- \( x = -6 + 5\sqrt{2} \)
- \( x = -6 - 5\sqrt{2} \)

Here are your responses filled in:

- \( x^2 + 12x + 36 \)
- \( 14 + 36 \)
- \( (x + 6)^2 \)
- \( 50 \)
- Take the square root of both sides.
- \( x + 6 = \pm \sqrt{50} \)
- \( x = -6 \pm 5\sqrt{2} \)

Final answers are:
- \( x = -6 + 5\sqrt{2} \) and \( x = -6 - 5\sqrt{2} \)

Answer 4

Sure! Here’s a simplified step-by-step solution for completing the square for the equation \(x^2 + 12x - 14 = 0\):

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

2. Rearrange to isolate the constant:
\[
x^2 + 12x = 14
\]

3. Complete the square:
- Take half of 12 (which is 6), square it (which is 36), and add it to both sides:
\[
x^2 + 12x + 36 = 14 + 36
\]

4. This gives:
\[
(x + 6)^2 = 50
\]

5. Take the square root:
\[
x + 6 = \pm \sqrt{50}
\]

6. Isolate \(x\):
\[
x = -6 \pm \sqrt{50}
\]

7. Simplify \(\sqrt{50}\) (which is \(5\sqrt{2}\)):
\[
x = -6 \pm 5\sqrt{2}
\]

Final answers:
- \( x = -6 + 5\sqrt{2} \)
- \( x = -6 - 5\sqrt{2} \)

Answer 5

We isolate the variable by subtracting 6 from both sides of the equation after taking the square root. Here's how that looks in detail:

Starting from:
\[
x + 6 = \pm \sqrt{50}
\]

Subtracting 6 from both sides gives:
\[
x = -6 \pm \sqrt{50}
\]

Then, since \(\sqrt{50} = 5\sqrt{2}\), we can further write it as:
\[
x = -6 \pm 5\sqrt{2}
\]

So, the step to isolate the variable is:

**We get isolate the variable by subtracting 6 from both sides.**

Final answers will still be:
- \( x = -6 + 5\sqrt{2} \)
- \( x = -6 - 5\sqrt{2} \)