Questions: Solve the quadratic equation by completing the square. x^2 - 2x - 2 = 0 x =

Solution Steps

To solve the quadratic equation \(x^2 - 2x - 2 = 0\) by completing the square, follow these steps:

1. Move the constant term to the right side of the equation.
2. Take half of the coefficient of \(x\), square it, and add it to both sides of the equation to complete the square.
3. Rewrite the left side as a perfect square trinomial.
4. Solve for \(x\) by taking the square root of both sides and isolating \(x\).

Starting with the equation: \[ x^2 - 2x - 2 = 0 \] we move the constant term to the right side: \[ x^2 - 2x = 2 \]

Next, we take half of the coefficient of \(x\) (which is \(-2\)), square it, and add it to both sides. Half of \(-2\) is \(-1\), and squaring it gives \(1\): \[ x^2 - 2x + 1 = 2 + 1 \] This simplifies to: \[ (x - 1)^2 = 3 \]

Now, we take the square root of both sides: \[ x - 1 = \pm \sqrt{3} \] Isolating \(x\) gives us: \[ x = 1 \pm \sqrt{3} \]

Final Answer