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).