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Consider the equation: x^2-4x+4=2x .Rewrite the equation by completing the square

A) x = -5 ± √3
B) x = 5 ± √3
C) x = -3 ± √5
D) x = 3 ± √5

1 Answer

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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.

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