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Solve by completing the square.\newlinej2+22j=−9j^2 + 22j = -9\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=−9j^2 + 22j = -9\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 99 to both sides to set the equation to zero. j2+22j+9=0j^2 + 22j + 9 = 0
  2. Add to complete square: Choose the number to add to both sides to complete the square.\newlineSince (222)2=121(\frac{22}{2})^2 = 121, add 121121 to both sides.\newlinej2+22j+121=9+121j^2 + 22j + 121 = 9 + 121\newlinej2+22j+121=130j^2 + 22j + 121 = 130
  3. Factor left side: Factor the left side of the equation.\newline(j+11)2=130(j + 11)^2 = 130
  4. Take square root: Take the square root of both sides of the equation.\newline(j+11)2=±130\sqrt{(j + 11)^2} = \pm\sqrt{130}\newlinej+11=±130j + 11 = \pm\sqrt{130}
  5. Solve for j: Solve for j by isolating the variable.\newlineSubtract 1111 from both sides.\newlinej=−11±130j = -11 \pm \sqrt{130}
  6. Calculate decimal values: Calculate the approximate decimal values of jj.130≈11.40\sqrt{130} \approx 11.40$j≈−11±11.40\$j \approx -11 \pm 11.40\)
  7. Find values of j: Find the two values of j.\newlinej≈−11+11.40j \approx -11 + 11.40 implies j≈0.40j \approx 0.40\newlinej≈−11−11.40j \approx -11 - 11.40 implies j≈−22.40j \approx -22.40\newlineValues of j: 0.400.40, −22.40-22.40

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