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Rewrite the equation by completing the square. {:[x^(2)+10 x+25=0],[(x+◻)^(2)=◻]:}

Rewrite the equation by completing the square.\newlinex2+10x+25=0x^2+10x+25=0\newline(x+□)2=□(x+\square)^2=\square

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Full solution

Q. Rewrite the equation by completing the square.\newlinex2+10x+25=0x^2+10x+25=0\newline(x+□)2=□(x+\square)^2=\square
  1. Step 11: Form a Perfect Square Trinomial: We start with the given quadratic equation x2+10x+25=0x^2 + 10x + 25 = 0. To complete the square, we need to form a perfect square trinomial on the left side of the equation.
  2. Step 22: Verify the Perfect Square Trinomial: The given equation is already a perfect square trinomial because (102)2=52=25(\frac{10}{2})^2 = 5^2 = 25, which is the constant term in the equation. Therefore, we can rewrite the equation as (x+5)2=0(x + 5)^2 = 0.
  3. Step 33: Recognize the Completed Square: Since we have the equation in the form of (x+5)2=0(x + 5)^2 = 0, we can see that the square has been completed. There is no need to add or subtract any terms, as the left side is already a perfect square.

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