To find the roots of the quadratic equation x^2 - 2x - 2 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the roots can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -2, and c = -2. Plugging these values into the quadratic formula, we get:
x = (-(-2) ± √((-2)^2 - 4(1)(-2))) / (2(1))
x = (2 ± √(4 + 8)) / 2
x = (2 ± √12) / 2
x = (2 ± 2√3) / 2
Simplifying further, we have:
x = 1 ± √3
So the roots of the equation x^2 - 2x - 2 = 0 are 1 + √3 and 1 - √3.