Let's solve the equation \( x^2 + 4x - 6 = 2 \) by completing the square.
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First, rearrange the equation: \[ x^2 + 4x - 6 - 2 = 0 \ x^2 + 4x - 8 = 0 \]
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Move \(-8\) to the other side: \[ x^2 + 4x = 8 \]
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Complete the square for the left side. Take half of the coefficient of \(x\) (which is \(4\)), square it, and add it inside the equation: \[ \left(\frac{4}{2}\right)^2 = 4 \] Add \(4\) to both sides: \[ x^2 + 4x + 4 = 8 + 4 \ (x + 2)^2 = 12 \]
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Take the square root of both sides: \[ x + 2 = \pm \sqrt{12} \ x + 2 = \pm 2\sqrt{3} \]
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Solve for \(x\): \[ x = -2 \pm 2\sqrt{3} \]
So the correct solutions are: \[ x = -2 + 2\sqrt{3}, \quad x = -2 - 2\sqrt{3} \]
Now let's compare the solutions with the provided expression \( x = -2 + 23 - \sqrt{}, -2 - 23 - \sqrt{} \). The expression seems to contain an error with the numbers and the format.
Therefore, the answer is:
Enter 2 for No.