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

1 answer

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