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Solve by completing the square.\newlinej2+4j=29j^2 + 4j = 29\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+4j=29j^2 + 4j = 29\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. Write equation in form: Write the equation in the form of j2+bj=cj^2 + bj = c. The given equation is already in this form: j2+4j=29j^2 + 4j = 29.
  2. Move constant term: Move the constant term to the right side of the equation.\newlineSubtract 2929 from both sides to isolate the jj terms.\newlinej2+4j−29=0j^2 + 4j - 29 = 0\newlinej2+4j=29j^2 + 4j = 29
  3. Complete the square: Complete the square by adding the square of half the coefficient of jj to both sides.\newlineThe coefficient of jj is 44, so half of it is 22, and the square of 22 is 44.\newlineAdd 44 to both sides of the equation.\newlinej2+4j+4=29+4j^2 + 4j + 4 = 29 + 4\newlinej2+4j+4=33j^2 + 4j + 4 = 33
  4. Factor left side: Factor the left side of the equation.\newlineThe left side is a perfect square trinomial.\newline(j+2)2=33(j + 2)^2 = 33
  5. Take square root: Take the square root of both sides of the equation.\newlineRemember to consider both the positive and negative square roots.\newline(j+2)2=±33\sqrt{(j + 2)^2} = \pm\sqrt{33}\newlinej+2=±33j + 2 = \pm\sqrt{33}
  6. Solve for jj: Solve for jj by isolating the variable.\newlineSubtract 22 from both sides of the equation.\newlinej+2−2=±33−2j + 2 - 2 = \pm\sqrt{33} - 2\newlinej=−2±33j = -2 \pm\sqrt{33}
  7. Calculate decimal values: Calculate the approximate decimal values of jj, rounded to the nearest hundredth.\newlinej≈−2+33≈−2+5.74≈3.74j \approx -2 + \sqrt{33} \approx -2 + 5.74 \approx 3.74\newlinej≈−2−33≈−2−5.74≈−7.74j \approx -2 - \sqrt{33} \approx -2 - 5.74 \approx -7.74

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