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Solve for mm. \newlinem2+20m+19=0m^2 + 20m + 19 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. \newlinem=m = ____

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Q. Solve for mm. \newlinem2+20m+19=0m^2 + 20m + 19 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. \newlinem=m = ____
  1. Identify quadratic equation: Identify the quadratic equation to solve.\newlineThe given quadratic equation is m2+20m+19=0m^2 + 20m + 19 = 0. We need to find two numbers that multiply to 1919 and add up to 2020.
  2. Find multiplying numbers: Find two numbers that multiply to 1919 and add up to 2020. The numbers 11 and 1919 multiply to 1919 (1×19=191 \times 19 = 19) and add up to 2020 (1+19=201 + 19 = 20).
  3. Rewrite quadratic equation: Rewrite the quadratic equation by splitting the middle term using the numbers found in Step 22.\newlinem2+20m+19=0m^2 + 20m + 19 = 0 can be rewritten as\newline m2+19m+1m+19=0m^2 + 19m + 1m + 19 = 0.
  4. Factor by grouping: Factor by grouping.\newlineGroup the terms to factor by common terms:\newline(m2+19m)+(1m+19)=0(m^2 + 19m) + (1m + 19) = 0\newlinem(m+19)+1(m+19)=0m(m + 19) + 1(m + 19) = 0\newline(m+1)(m+19)=0(m + 1)(m + 19) = 0
  5. Solve for m: Solve for m using the zero product property.\newlineSet each factor equal to zero and solve for m:\newlinem+1=0m + 1 = 0 or m+19=0m + 19 = 0\newlinem=−1m = -1 or m=−19m = -19

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