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Rewrite the equation by completing the square. {:[x^(2)+3x-28=0],[(x+◻)^(2)=◻]:}

Rewrite the equation by completing the square.\newlinex2+3x−28=0x^2+3x-28=0\newline(x+□)2=□(x+\square)^2=\square

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Full solution

Q. Rewrite the equation by completing the square.\newlinex2+3x−28=0x^2+3x-28=0\newline(x+□)2=□(x+\square)^2=\square
  1. Write Original Equation: Write down the original equation.\newlineThe original equation is x2+3x−28=0x^2 + 3x - 28 = 0.
  2. Move Constant Term: Move the constant term to the other side of the equation.\newlineTo complete the square, we need to have the xx-terms on one side and the constant on the other side. So we add 2828 to both sides of the equation:\newlinex2+3x=28x^2 + 3x = 28
  3. Find Completion Number: 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. In this case, b=3b = 3, so (32)2=(1.5)2=2.25(\frac{3}{2})^2 = (1.5)^2 = 2.25.
  4. Add Completion Number: Add (b2)2(\frac{b}{2})^2 to both sides of the equation.\newlineWe add 2.252.25 to both sides of the equation to complete the square:\newlinex2+3x+2.25=28+2.25x^2 + 3x + 2.25 = 28 + 2.25
  5. Write Left Side: Write the left side of the equation as a square of a binomial.\newlineThe left side of the equation is now a perfect square trinomial, which can be written as the square of a binomial:\newline(x+1.5)2=30.25(x + 1.5)^2 = 30.25
  6. Simplify Right Side: Simplify the right side of the equation.\newlineWe simplify the right side of the equation to get the final completed square form:\newline(x+1.5)2=30.25(x + 1.5)^2 = 30.25

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