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Solve by completing the square.\newlinej2−10j−21=0j^2 - 10j - 21 = 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.\newlinej2−10j−21=0j^2 - 10j - 21 = 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 2121 to both sides to set the equation up for completing the square. j2−10j−21+21=0+21j^2 - 10j - 21 + 21 = 0 + 21 j2−10j=21j^2 - 10j = 21
  2. Add 2121: Choose the number to add to both sides to complete the square.\newlineSince (−102)2=25\left(-\frac{10}{2}\right)^2 = 25, add 2525 to both sides.\newlinej2−10j+25=21+25j^2 - 10j + 25 = 21 + 25\newlinej2−10j+25=46j^2 - 10j + 25 = 46
  3. Choose number: Factor the left side of the equation.\newlinej2−10j+25j^2 - 10j + 25 is a perfect square trinomial.\newline(j−5)2=46(j - 5)^2 = 46
  4. Factor left side: Take the square root of both sides of the equation.\newline(j−5)2=±46\sqrt{(j - 5)^2} = \pm\sqrt{46}\newlinej−5=±46j - 5 = \pm\sqrt{46}
  5. Take square root: Solve for jj.\newlineAdd 55 to both sides of the equation to isolate jj.\newlinej−5+5=±46+5j - 5 + 5 = \pm\sqrt{46} + 5\newlinej=5±46j = 5 \pm \sqrt{46}
  6. Solve for jj: Calculate the approximate values of jj.\newlineSince 46\sqrt{46} is approximately 6.786.78 (rounded to the nearest hundredth), we have:\newlinej≈5+6.78j \approx 5 + 6.78 or j≈5−6.78j \approx 5 - 6.78\newlinej≈11.78j \approx 11.78 or j≈−1.78j \approx -1.78

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