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Rewrite the equation by completing the square. {:[x^(2)-2x+1=0],[(x+◻)^(2)=◻]:}

Rewrite the equation by completing the square.\newlinex2−2x+1=0x^2-2x+1=0\newline(x+□)2=□(x+\square)^2=\square

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Full solution

Q. Rewrite the equation by completing the square.\newlinex2−2x+1=0x^2-2x+1=0\newline(x+□)2=□(x+\square)^2=\square
  1. Identify equation: Identify the equation to be rewritten by completing the square.\newlineWe have the equation x2−2x+1=0x^2 - 2x + 1 = 0.
  2. Recognize perfect square: Recognize that the equation is already a perfect square trinomial.\newlineThe equation x2−2x+1x^2 - 2x + 1 is a perfect square because it can be factored into (x−1)2(x - 1)^2.
  3. Rewrite in completed square form: Rewrite the equation in completed square form.\newlineSince x2−2x+1x^2 - 2x + 1 is already a perfect square, it can be written as (x−1)2=0(x - 1)^2 = 0.
  4. Verify completed square form: Verify the completed square form.\newlineTo check, we can expand (x−1)2(x - 1)^2 to get x2−2x+1x^2 - 2x + 1, which matches the original equation.

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