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Rewrite the equation by completing the square. {:[x^(2)+10 x+24=0],[(x+◻)^(2)=◻]:}

Rewrite the equation by completing the square.\newlinex2+10x+24=0x^2+10x+24=0\newline(x+□)2=□(x+\square)^2=\square

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Full solution

Q. Rewrite the equation by completing the square.\newlinex2+10x+24=0x^2+10x+24=0\newline(x+□)2=□(x+\square)^2=\square
  1. Write quadratic equation: Write down the given quadratic equation.\newlineWe are given the quadratic equation x2+10x+24=0x^2 + 10x + 24 = 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 x2x^2 and xx terms on one side and the constant on the other side. So we subtract 2424 from both sides of the equation.\newlinex2+10x=−24x^2 + 10x = -24
  3. Find completing number: Find the number to complete the square.\newlineTo complete the square, we need to add (b/2)2(b/2)^2 to both sides of the equation, where bb is the coefficient of xx. In this case, b=10b = 10.\newline(10/2)2=(5)2=25(10/2)^2 = (5)^2 = 25
  4. Add completing number: Add (b2)2(\frac{b}{2})^2 to both sides of the equation.\newlineWe add 2525 to both sides of the equation to complete the square.\newlinex2+10x+25=−24+25x^2 + 10x + 25 = -24 + 25
  5. Write as square of binomial: 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+5)2=1(x + 5)^2 = 1
  6. Check completed square equation: Check the completed square equation.\newlineWe have the equation in the form of (x+p)2=q(x + p)^2 = q, where pp is half of the coefficient of xx from the original equation, and qq is the constant term after completing the square.\newline(x+5)2=1(x + 5)^2 = 1\newlineThis is the completed square form of the original equation.

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