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

Let's fill in 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 right side:
\[
x^2 + 12x = 14
\]

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

4. This simplifies to:
\[
x^2 + 12x + 36 = 50
\]

5. We can now factor the left-hand side:
\[
(x + 6)^2 = 50
\]

6. At this point, we need to take the square root of both sides:
\[
x + 6 = \pm \sqrt{50}
\]
(Note: \( \sqrt{50} = 5\sqrt{2} \))

7. After that is done, we will have:
\[
x + 6 = 5\sqrt{2} \quad \text{or} \quad x + 6 = -5\sqrt{2}
\]

8. To isolate the variable \( x \), we subtract 6 from both sides:
\[
x = -6 + 5\sqrt{2} \quad \text{or} \quad x = -6 - 5\sqrt{2}
\]

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