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Rewrite the equation by completing the square. {:[x^(2)-14 x+40=0],[(x+◻)^(2)=◻]:}

Rewrite the equation by completing the square.\newlinex2−14x+40=0x^2-14x+40=0\newline(x+□)2=□(x+\square)^2=\square

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Full solution

Q. Rewrite the equation by completing the square.\newlinex2−14x+40=0x^2-14x+40=0\newline(x+□)2=□(x+\square)^2=\square
  1. Rewrite equation: Rewrite the equation in the form of x2+bx=cx^2 + bx = c.\newlineWe start with the given equation x2−14x+40=0x^2 - 14x + 40 = 0 and move the constant term to the other side to prepare for completing the square.\newlinex2−14x=−40x^2 - 14x = -40
  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. In this case, b=−14b = -14.\newline(−142)2=(−7)2=49(-\frac{14}{2})^2 = (-7)^2 = 49
  3. Add square to equation: Add the square to both sides of the equation.\newlineWe add 4949 to both sides of the equation to complete the square.\newlinex2−14x+49=−40+49x^2 - 14x + 49 = -40 + 49\newlinex2−14x+49=9x^2 - 14x + 49 = 9
  4. Factor left side of equation: Factor the left side of the equation.\newlineThe left side of the equation is now a perfect square trinomial, so we can factor it as the square of a binomial.\newline(x−7)2=9(x - 7)^2 = 9
  5. Write completed square form: Write the completed square form of the equation.\newlineThe equation is now in the completed square form.\newline(x−7)2=9(x - 7)^2 = 9

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