Final answer:
To complete the square for f(x)=x^2-8x-2, move the constant to the right, add 16 to both sides, and rewrite as a perfect square trinomial, resulting in f(x) = (x - 4)^2 - 18.
Step-by-step explanation:
To rewrite the equation by completing the square for the equation f(x)=x2-8x-2, you should first move the constant term to the right side of the equation:
x2 - 8x = 2
Next, you need to add a number to both sides of the equation to make the left side a perfect square trinomial. You determine this number by taking half of the coefficient of x, which is -4, and squaring it, giving you 16.
Add 16 to both sides:
x2 - 8x + 16 = 2 + 16
The left side is now a perfect square trinomial:
(x - 4)2 = 18
Therefore, the complete square form of the equation is f(x) = (x - 4)2 - 18.