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Solve for nn.\newlinen2+13n+22=0n^2 + 13n + 22 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. \newlineIf there are multiple solutions, separate them with commas.\newlinen=n = ____

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Q. Solve for nn.\newlinen2+13n+22=0n^2 + 13n + 22 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. \newlineIf there are multiple solutions, separate them with commas.\newlinen=n = ____
  1. Identify quadratic equation: Identify the quadratic equation to be solved.\newlineThe given quadratic equation is n2+13n+22=0n^2 + 13n + 22 = 0. We need to find two numbers that multiply to 2222 and add up to 1313.
  2. Factor quadratic equation: Factor the quadratic equation.\newlineWe are looking for two numbers that multiply to give 2222 and add to give 1313. The numbers 1111 and 22 satisfy these conditions because 11×2=2211 \times 2 = 22 and 11+2=1311 + 2 = 13.\newlineSo, we can write the quadratic equation as (n+11)(n+2)=0(n + 11)(n + 2) = 0.
  3. Solve using zero product property: Solve for nn using the zero product property.\newlineIf (n+11)(n+2)=0(n + 11)(n + 2) = 0, then either n+11=0n + 11 = 0 or n+2=0n + 2 = 0.
  4. Solve first equation: Solve the first equation n+11=0n + 11 = 0.\newlineSubtract 1111 from both sides to isolate nn.\newlinen+11−11=0−11n + 11 - 11 = 0 - 11\newlinen=−11n = -11
  5. Solve second equation: Solve the second equation n+2=0n + 2 = 0. Subtract 22 from both sides to isolate nn. n+2−2=0−2n + 2 - 2 = 0 - 2 n=−2n = -2

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