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Solve for jj.\newlinej2−22j+21=0j^2 - 22j + 21 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinej=j = ____

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Solve a quadratic equation by factoringright chevron icon

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Q. Solve for jj.\newlinej2−22j+21=0j^2 - 22j + 21 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinej=j = ____
  1. Identify Quadratic Equation: Identify the quadratic equation to be solved.\newlineThe given quadratic equation is j2−22j+21=0j^2 - 22j + 21 = 0. We need to find two numbers that multiply to 2121 and add up to −22-22.
  2. Find Multiplying Numbers: Find two numbers that multiply to 2121 and add up to −22-22. The numbers −1-1 and −21-21 multiply to 2121 and add up to −22-22.
  3. Rewrite Using Numbers: Rewrite the quadratic equation by splitting the middle term using the numbers found in Step 22.\newlinej2−1j−21j+21=0j^2 - 1j - 21j + 21 = 0
  4. Factor by Grouping: Factor by grouping.\newlineGroup the terms to factor by common terms:\newline(j2−1j)−(21j−21)=0(j^2 - 1j) - (21j - 21) = 0\newlinej(j−1)−21(j−1)=0j(j - 1) - 21(j - 1) = 0
  5. Factor Out Common Factor: Factor out the common binomial factor.\newline(j−1)(j−21)=0(j - 1)(j - 21) = 0
  6. Set and Solve Equations: Set each factor equal to zero and solve for jj.j−1=0j - 1 = 0 or j−21=0j - 21 = 0
  7. Solve for j=1j=1: Solve the first equation for jj.j−1+1=0+1j - 1 + 1 = 0 + 1j=1j = 1
  8. Solve for j=21j=21: Solve the second equation for jj.j−21+21=0+21j - 21 + 21 = 0 + 21j=21j = 21

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