Final answer:
To rewrite the equation by completing the square, we rearrange and add the appropriate constant to form a perfect square trinomial. Upon isolating the perfect square and taking the square root, the solution to the equation is D) x = 3 ± √5.
Step-by-step explanation:
To rewrite the equation x^2-4x+4=2x by completing the square, we need to form a perfect square trinomial on one side of the equation and then solve for x. First, let's subtract 2x from both sides to bring the terms involving x together.
x^2 - 4x - 2x + 4 = 0
x^2 - 6x + 4 = 0
Now, we divide the coefficient of x, which is 6, by 2 and square the result to find the number that will complete the square.
(6/2)^2 = 9
Next, we add and subtract this new number (9) inside the equation to maintain equality.
x^2 - 6x + 9 - 9 + 4 = 0
(x - 3)^2 - 5 = 0
Now we isolate the perfect square and take the square root of both sides.
(x - 3)^2 = 5
x - 3 = ±5√5
Finally, we solve for x.
x = 3 ± √5
Thus, the correct answer is D) x = 3 ± √5.