Solve the quadratic equation by completing the square.x squaredminus4xequals2Question content area bottomPart 1xequalsenter your response here​(Simplify your answer. Type an exact​ answer, using radicals as needed. Use a comma to separate answers as​ needed.)

Answer 1

To solve the quadratic equation \(x^2 - 4x = 2\) by completing the square, follow these steps:

1. Move the constant to the other side: \[ x^2 - 4x - 2 = 0 \]

2. Prepare to complete the square: We take the coefficient of \(x\) (which is \(-4\)), halve it (which gives \(-2\)), and then square it (which gives \(4\)).

3. Add and subtract this square inside the equation: \[ x^2 - 4x + 4 - 4 - 2 = 0 \] This can be rearranged as: \[ (x - 2)^2 - 6 = 0 \]

4. Set the equation to zero: \[ (x - 2)^2 = 6 \]

5. Take the square root of both sides: \[ x - 2 = \pm \sqrt{6} \]

6. Solve for \(x\): \[ x = 2 \pm \sqrt{6} \]

Therefore, the solutions are: \[ x = 2 + \sqrt{6}, \quad x = 2 - \sqrt{6} \]

So the final answer is: \[ x = 2 + \sqrt{6}, 2 - \sqrt{6} \]