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Rewrite the equation by completing the square. {:[x^(2)+10 x+21=0],[(x+◻)^(2)=◻]:}

Rewrite the equation by completing the square.\newlinex2+10x+21=0(x+□)2=□ \begin{array}{l} x^{2}+10 x+21=0 \\ (x+\square)^{2}=\square \end{array}

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Q. Rewrite the equation by completing the square.\newlinex2+10x+21=0(x+□)2=□ \begin{array}{l} x^{2}+10 x+21=0 \\ (x+\square)^{2}=\square \end{array}
  1. Rewrite equation in form: Rewrite the equation in the form of x2+bx=cx^2 + bx = c.\newlineSubtract 2121 from both sides to set the equation up for completing the square.\newlinex2+10x+21−21=0−21x^2 + 10x + 21 - 21 = 0 - 21\newlinex2+10x=−21x^2 + 10x = -21
  2. Subtract to set up: Find the number to complete the square.\newlineTo complete the square, we need to add (b2)2(\frac{b}{2})^2 to both sides of the equation, where bb is the coefficient of xx.\newlineIn this case, b=10b = 10, so (102)2=(5)2=25(\frac{10}{2})^2 = (5)^2 = 25.
  3. Find number to complete: Add 2525 to both sides of the equation to complete the square.\newlinex2+10x+25=−21+25x^2 + 10x + 25 = -21 + 25\newlinex2+10x+25=4x^2 + 10x + 25 = 4
  4. Add to complete square: Factor the left side of the equation.\newlineThe left side of the equation is now a perfect square trinomial, so it can be factored into (x+5)2(x + 5)^2.\newline(x+5)2=4(x + 5)^2 = 4
  5. Factor left side of equation: Write the completed square form of the equation.\newlineThe equation in completed square form is (x+5)2=4(x + 5)^2 = 4.

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