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Solve by completing the square.\newlinex2−22x=−13x^2 - 22x = -13\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinex=x = _____ or x=x = _____

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Q. Solve by completing the square.\newlinex2−22x=−13x^2 - 22x = -13\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinex=x = _____ or x=x = _____
  1. Rewrite equation: Rewrite the equation in the form of x2+bx=cx^2 + bx = c. Add 1313 to both sides to move the constant term to the right side. x2−22x+13=0x^2 - 22x + 13 = 0
  2. Complete the square: To complete the square, find the value that needs to be added to both sides of the equation.\newlineSince (−222)2=121(-\frac{22}{2})^2 = 121, add 121121 to both sides.\newlinex2−22x+121=13+121x^2 - 22x + 121 = 13 + 121\newlinex2−22x+121=134x^2 - 22x + 121 = 134
  3. Factor trinomial: Factor the left side of the equation as a perfect square trinomial.\newlinex2−22x+121=(x−11)2x^2 - 22x + 121 = (x - 11)^2\newlineSo the equation becomes:\newline(x−11)2=134(x - 11)^2 = 134
  4. Take square root: Take the square root of both sides of the equation.\newline(x−11)2=±134\sqrt{(x - 11)^2} = \pm\sqrt{134}\newlinex−11=±134x - 11 = \pm\sqrt{134}
  5. Solve for x: Solve for x by adding 1111 to both sides of the equation.\newlinex=11±134x = 11 \pm \sqrt{134}
  6. Calculate solutions: Calculate the approximate decimal values of the square root of 134134 and add 1111 to find the two solutions for xx.\newline134\sqrt{134} is approximately 11.5811.58.\newlinex≈11+11.58x \approx 11 + 11.58 or x≈11−11.58x \approx 11 - 11.58\newlinex≈22.58x \approx 22.58 or x≈−0.58x \approx -0.58

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