Complete the square to solve the following quadratic equation: x2+4x−6=2

To solve the quadratic equation \( x^2 + 4x - 6 = 2 \) by completing the square, we first need to rearrange the equation:

\[
x^2 + 4x - 6 - 2 = 0 \implies x^2 + 4x - 8 = 0
\]

Next, we move the constant term to the other side:

\[
x^2 + 4x = 8
\]

Now, we complete the square. To do this, we take the coefficient of \( x \), which is 4, divide it by 2 to get 2, and then square it to get 4.

Now we add and subtract this square inside the equation:

\[
x^2 + 4x + 4 - 4 = 8
\]

This simplifies to:

\[
(x + 2)^2 - 4 = 8
\]

Now add 4 to both sides:

\[
(x + 2)^2 = 12
\]

Now, take the square root of both sides:

\[
x + 2 = \pm \sqrt{12}
\]

Simplifying \( \sqrt{12} \) gives \( 2\sqrt{3} \):

\[
x + 2 = \pm 2\sqrt{3}
\]

Now, subtract 2 from both sides:

\[
x = -2 \pm 2\sqrt{3}
\]

This means the solutions are:

\[
x = -2 + 2\sqrt{3}, \quad x = -2 - 2\sqrt{3}
\]

The provided solutions \( x = -2 + 23 - \sqrt{ } \) and \( x = -2 - 23 - \sqrt{ } \) appear to be incorrect due to the presence of "23" and the lack of proper notation for \(\sqrt{12}\).

Therefore, the answer is:

**2** (No).