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Solve for nn. \newlinen2−12n+11=0n^2 - 12n + 11 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. \newlinen=n = ____

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Q. Solve for nn. \newlinen2−12n+11=0n^2 - 12n + 11 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. \newlinen=n = ____
  1. Find Numbers: Find two numbers that multiply to 1111 and add up to −12-12.
  2. Identify Numbers: The numbers are −11-11 and −1-1 because −11×−1=11-11 \times -1 = 11 and −11+−1=−12-11 + -1 = -12.
  3. Rewrite Equation: Rewrite the equation by splitting the middle term using the numbers found in Step 22.\newlinen2−11n−1n+11=0n^2 - 11n - 1n + 11 = 0
  4. Factor by Grouping: Factor by grouping.\newline(n2−11n)+(−1n+11)=0(n^2 - 11n) + (-1n + 11) = 0\newlinen(n−11)−1(n−11)=0n(n - 11) - 1(n - 11) = 0\newline(n−1)(n−11)=0(n - 1)(n - 11) = 0
  5. Set Equal and Solve: Set each factor equal to zero and solve for nn.n−1=0n - 1 = 0 or n−11=0n - 11 = 0n=1n = 1 or n=11n = 11

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