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Solve for nn. \newlinen2−9n+14=0n^2 - 9n + 14 = 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. \newlinen2−9n+14=0n^2 - 9n + 14 = 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. Identify Equation: Identify the quadratic equation to be solved.\newlineThe given quadratic equation is n2−9n+14=0n^2 - 9n + 14 = 0. We need to find two numbers that multiply to give 1414 and add up to give −9-9.
  2. Find Numbers: Find two numbers that multiply to 1414 and add up to −9-9. The numbers that satisfy these conditions are −7-7 and −2-2 because (−7)×(−2)=14(-7) \times (-2) = 14 and (−7)+(−2)=−9(-7) + (-2) = -9.
  3. Rewrite Equation: Rewrite the quadratic equation by splitting the middle term using the numbers found in Step 22. n2−7n−2n+14=0n^2 - 7n - 2n + 14 = 0
  4. Factor by Grouping: Factor by grouping.\newlineGroup the terms to factor by common terms:\newline(n2−7n)−(2n−14)=0(n^2 - 7n) - (2n - 14) = 0\newlinen(n−7)−2(n−7)=0n(n - 7) - 2(n - 7) = 0
  5. Factor Common Factor: Factor out the common binomial factor.\newline(n−7)(n−2)=0(n - 7)(n - 2) = 0
  6. Set Equal and Solve: Set each factor equal to zero and solve for nn.n−7=0n - 7 = 0 or n−2=0n - 2 = 0If n−7=0n - 7 = 0, then n=7n = 7.If n−2=0n - 2 = 0, then n=2n = 2.

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