Final answer:
The quadratic equation x^2-8x+20 can be expressed as (x-4)^2 + 4, which fits the form (x-a)^2 + a by completing the square method.
Step-by-step explanation:
The equation x^2-8x+20 can be rewritten in the form (x-a)^2 + a by completing the square. First, we should find the value that makes x^2-8x a perfect square trinomial. We take half of the coefficient of x, which is -4, and square it to get 16. Adding and subtracting this number inside the quadratic equation gives us:
- x^2 - 8x + 16 - 16 + 20
- (x - 4)^2 + 4
Thus, we've successfully expressed the equation in the desired form with a=4. Completing the square is a common method used for solving quadratic equations without the quadratic formula and is useful in transforming equations into different forms.