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Rewrite the equation by completing the square. {:[x^(2)-14 x+33=0],[(x+◻)^(2)=◻]:}

Rewrite the equation by completing the square.\newlinex2−14x+33=0x^2-14x+33=0\newline(x+□)2=□(x+\square)^2=\square

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Full solution

Q. Rewrite the equation by completing the square.\newlinex2−14x+33=0x^2-14x+33=0\newline(x+□)2=□(x+\square)^2=\square
  1. Rewrite equation: Rewrite the equation in the form of x2+bx=cx^2 + bx = c.\newlineSubtract 3333 from both sides to set the equation up for completing the square.\newlinex2−14x+33−33=0−33x^2 - 14x + 33 - 33 = 0 - 33\newlinex2−14x=−33x^2 - 14x = -33
  2. Find completing square 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.\newlineIn this case, b=−14b = -14, so (b2)2=(−142)2=(−7)2=49(\frac{b}{2})^2 = (\frac{-14}{2})^2 = (-7)^2 = 49.
  3. Add completing square number: Add 4949 to both sides of the equation.\newlinex2−14x+49=−33+49x^2 - 14x + 49 = -33 + 49\newlinex2−14x+49=16x^2 - 14x + 49 = 16
  4. Factor left side: Factor the left side of the equation.\newlineThe left side of the equation is now a perfect square trinomial.\newline(x−7)2=16(x - 7)^2 = 16
  5. Write completed square form: Write the completed square form of the equation.\newlineThe equation in completed square form is:\newline(x−7)2=16(x - 7)^2 = 16

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