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Rewrite the equation by completing the square. {:[x^(2)+2x-3=0],[(x+◻)^(2)=◻]:}

Rewrite the equation by completing the square.\newlinex2+2x−3=0(x+□)2=□ \begin{array}{l} x^{2}+2 x-3=0 \\ (x+\square)^{2}=\square \end{array}

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Q. Rewrite the equation by completing the square.\newlinex2+2x−3=0(x+□)2=□ \begin{array}{l} x^{2}+2 x-3=0 \\ (x+\square)^{2}=\square \end{array}
  1. Rewrite equation in standard form: Rewrite the equation in the form of x2+bx=cx^2 + bx = c.\newlineAdd 33 to both sides to move the constant term to the right side of the equation.\newlinex2+2x−3+3=0+3x^2 + 2x - 3 + 3 = 0 + 3\newlinex2+2x=3x^2 + 2x = 3
  2. Add 33 to both sides: Choose the number to complete the square.\newlineSince (22)2=1(\frac{2}{2})^2 = 1, add 11 to both sides of the equation to complete the square.\newlinex2+2x+1=3+1x^2 + 2x + 1 = 3 + 1\newlinex2+2x+1=4x^2 + 2x + 1 = 4
  3. Complete the square: Identify the equation after factoring the left side.\newlineThe left side is a perfect square trinomial.\newline(x+1)2=4(x + 1)^2 = 4
  4. Identify factored equation: The equation is now in the completed square form. (x+1)2=4(x + 1)^2 = 4

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