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Solve by completing the square.\newlinej2−22j+19=0j^2 - 22j + 19 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinej=j = _____ or j=j = _____

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Q. Solve by completing the square.\newlinej2−22j+19=0j^2 - 22j + 19 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinej=j = _____ or j=j = _____
  1. Rewrite equation: Rewrite the equation in the form of j2+bj=cj^2 + bj = c. The given equation is already in this form: j2−22j+19=0j^2 - 22j + 19 = 0. Subtract 1919 from both sides to set the equation up for completing the square. j2−22j=−19j^2 - 22j = -19
  2. Subtract and set up: Find the number to add to both sides to complete the square.\newlineTo complete the square, we need to add (b/2)2(b/2)^2 to both sides, where bb is the coefficient of jj. In this case, b=−22b = -22.\newline(−22/2)2=(−11)2=121(-22/2)^2 = (-11)^2 = 121\newlineAdd 121121 to both sides of the equation.\newlinej2−22j+121=−19+121j^2 − 22j + 121 = -19 + 121\newlinej2−22j+121=102j^2 − 22j + 121 = 102
  3. Find completing square number: Factor the left side of the equation.\newlineThe left side of the equation is now a perfect square trinomial.\newline(j−11)2=102(j - 11)^2 = 102
  4. Factor left side: Take the square root of both sides.\newlineTo solve for jj, take the square root of both sides of the equation.\newline(j−11)2=±102\sqrt{(j − 11)^2} = \pm\sqrt{102}\newlinej−11=±102j − 11 = \pm\sqrt{102}
  5. Take square root: Solve for jj.\newlineAdd 1111 to both sides of the equation to isolate jj.\newlinej=11±102j = 11 \pm \sqrt{102}\newlineTo find the decimal approximation, calculate the square root of 102102 and round to the nearest hundredth.\newline102≈10.10\sqrt{102} \approx 10.10\newlinej≈11±10.10j \approx 11 \pm 10.10
  6. Solve for jj: Find the two values of jj.
    j≈11+10.10j \approx 11 + 10.10 implies j≈21.10j \approx 21.10.
    j≈11−10.10j \approx 11 - 10.10 implies j≈0.90j \approx 0.90.
    Values of jj: 21.1021.10, 0.900.90

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