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Solve for ss.\newline4s2−35s−9=04s^2 - 35s - 9 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlines=s = ____

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Full solution

Q. Solve for ss.\newline4s2−35s−9=04s^2 - 35s - 9 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlines=s = ____
  1. Rewrite equation with split terms: Now, rewrite the equation by splitting the middle term using the numbers we found: 4s2−36s+s−9=04s^2 - 36s + s - 9 = 0.
  2. Factor by grouping: Next, factor by grouping: (4s2−36s)+(s−9)(4s^2 - 36s) + (s - 9). Take out the common factor from each group: 4s(s−9)+1(s−9)4s(s - 9) + 1(s - 9).
  3. Common factor extraction: Now we have a common factor of (s−9)(s - 9), so factor it out: (4s+1)(s−9)=0(4s + 1)(s - 9) = 0.
  4. Factor out common factor: Set each factor equal to zero: 4s+1=04s + 1 = 0 and s−9=0s - 9 = 0.
  5. Set factors equal to zero: Solve 4s+1=04s + 1 = 0: Subtract 11 from both sides to get 4s=−14s = -1, then divide by 44 to get s=−14s = -\frac{1}{4}.
  6. Solve for 4s+14s + 1: Solve s−9=0s - 9 = 0: Add 99 to both sides to get s=9s = 9.

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