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Rewrite the equation by completing the square. {:[x^(2)-4x=0],[(x+◻)^(2)=◻]:}

Rewrite the equation by completing the square.\newlinex2−4x=0x^2 - 4x = 0\newline(x+□)2=□(x + \square)^2 = \square

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Full solution

Q. Rewrite the equation by completing the square.\newlinex2−4x=0x^2 - 4x = 0\newline(x+□)2=□(x + \square)^2 = \square
  1. Finding the Perfect Square Trinomial: To complete the square, we need to find a number to add to both sides of the equation x2−4x=0x^2 - 4x = 0 so that the left side becomes a perfect square trinomial. The number we need to add is the square of half the coefficient of xx, which is (42)2=22=4(\frac{4}{2})^2 = 2^2 = 4.
  2. Adding 44 to Both Sides: Add 44 to both sides of the equation to complete the square on the left side.x2−4x+4=0+4x^2 - 4x + 4 = 0 + 4
  3. Factoring the Perfect Square Trinomial: Now, the left side of the equation is a perfect square trinomial, which can be factored into (x−2)2(x - 2)^2.(x−2)2=4(x - 2)^2 = 4
  4. Completing the Square: We have now rewritten the original equation by completing the square. The completed square form of the equation is (x−2)2=4(x - 2)^2 = 4.

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