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Solve by completing the square.\newlinej2−16j−29=0j^2 - 16j - 29 = 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.\newlinej2−16j−29=0j^2 - 16j - 29 = 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. Add 2929 to both sides to set the equation up for completing the square. j2−16j−29+29=0+29j^2 - 16j - 29 + 29 = 0 + 29 j2−16j=29j^2 - 16j = 29
  2. Add 2929: Choose the number to add to both sides to complete the square.\newlineSince (−162)2=64\left(-\frac{16}{2}\right)^2 = 64, add 6464 to both sides.\newlinej2−16j+64=29+64j^2 - 16j + 64 = 29 + 64\newlinej2−16j+64=93j^2 - 16j + 64 = 93
  3. Choose Number to Add: Factor the left side of the equation.\newlinej2−16j+64=93j^2 - 16j + 64 = 93\newline(j−8)2=93(j - 8)^2 = 93
  4. Factor Left Side: Take the square root of both sides of the equation.\newline(j−8)2=±93\sqrt{(j - 8)^2} = \pm\sqrt{93}\newlinej−8=±93j - 8 = \pm\sqrt{93}
  5. Take Square Root: Solve for jj by adding 88 to both sides of the equation.\newlinej−8+8=±93+8j - 8 + 8 = \pm\sqrt{93} + 8\newlinej=8±93j = 8 \pm \sqrt{93}
  6. Solve for jj: Calculate the approximate decimal values of jj, rounded to the nearest hundredth.\newlinej≈8+93j \approx 8 + \sqrt{93} or j≈8−93j \approx 8 - \sqrt{93}\newlinej≈8+9.64j \approx 8 + 9.64 or j≈8−9.64j \approx 8 - 9.64\newlinej≈17.64j \approx 17.64 or j≈−1.64j \approx -1.64

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