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Rewrite the equation by completing the square. {:[x^(2)+12 x+36=0],[(x+◻)^(2)=◻]:}

Rewrite the equation by completing the square.\newlinex2+12x+36=0x^2+12x+36=0\newline(x+□)2=□(x+\square)^2=\square

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Full solution

Q. Rewrite the equation by completing the square.\newlinex2+12x+36=0x^2+12x+36=0\newline(x+□)2=□(x+\square)^2=\square
  1. Identify coefficient of x: We start with the given quadratic equation x2+12x+36=0x^2 + 12x + 36 = 0 and identify the coefficient of xx, which is 1212.
  2. Find perfect square trinomial: To complete the square, we need to find a number that, when added and subtracted to the equation, forms a perfect square trinomial. This number is (122)2=62=36(\frac{12}{2})^2 = 6^2 = 36.
  3. Equation is already a perfect square trinomial: We notice that the given equation already has +36+36 as the constant term, which is the number we found in the previous step. This means the equation is already a perfect square trinomial.
  4. Rewrite the equation: We can rewrite the equation as (x+6)2=0(x + 6)^2 = 0, since (x+6)(x+6)(x + 6)(x + 6) expands to x2+12x+36x^2 + 12x + 36.

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