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Solve for jj. \newline16j2−25=016j^2 - 25 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. \newlinej=j = ____

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Full solution

Q. Solve for jj. \newline16j2−25=016j^2 - 25 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. \newlinej=j = ____
  1. Recognize difference of squares: First, let's recognize that 16j2−2516j^2 - 25 is a difference of squares, which can be factored into (4j+5)(4j−5)(4j + 5)(4j - 5).
  2. Set equations equal to zero: Set each factor equal to zero: 4j+5=04j + 5 = 0 and 4j−5=04j - 5 = 0.
  3. Solve first equation: Solve the first equation 4j+5=04j + 5 = 0: Subtract 55 from both sides to get 4j=−54j = -5.
  4. Isolate variable jj: Divide both sides by 44 to isolate jj: j=−54j = -\frac{5}{4}.
  5. Solve second equation: Now solve the second equation 4j−5=04j - 5 = 0: Add 55 to both sides to get 4j=54j = 5.
  6. Isolate variable jj: Divide both sides by 44 to isolate jj: j=54j = \frac{5}{4}.

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