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Solve by completing the square.\newlinej2−26j=−27j^2 - 26j = -27\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.\newlinej2−26j=−27j^2 - 26j = -27\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. Add 2727 to both sides to set the equation to zero. j2−26j+27=0j^2 - 26j + 27 = 0
  2. Complete the square: Choose the equation after completing the square.\newlineSince (−262)2=169(-\frac{26}{2})^2 = 169, add 169169 to both sides to complete the square.\newlinej2−26j+169=27+169j^2 − 26j + 169 = 27 + 169\newlinej2−26j+169=196j^2 − 26j + 169 = 196
  3. Factor left side: Identify the equation after factoring the left side.\newlinej2−26j+169=196j^2 - 26j + 169 = 196\newline(j−13)2=196(j - 13)^2 = 196
  4. Take square root: Identify the equation after taking the square root on both sides.\newlineTake the square root of both sides of the equation.\newline(j−13)2=196\sqrt{(j − 13)^2} = \sqrt{196}\newlinej−13=±196j − 13 = \pm\sqrt{196}\newlinej−13=±14j − 13 = \pm14
  5. Isolate variable: Choose the equation after isolating the variable jj. To isolate jj, add 1313 to both sides of the equation. j−13+13=±14+13j - 13 + 13 = \pm 14 + 13 j=13±14j = 13 \pm 14
  6. Find values of j: What are the two values of j?
    j = 13+1413 + 14 implies j = 2727.
    j = 13−1413 - 14 implies j = −1-1.
    Values of j: 2727, −1-1

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