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Solve for jj.\newlinej2+8j+15=0j^2 + 8j + 15 = 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+8j+15=0j^2 + 8j + 15 = 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+8j+15=0j^2 + 8j + 15 = 0. We need to find values of jj that satisfy this equation.
  2. Factor Equation: Factor the quadratic equation.\newlineWe need to find two numbers that multiply to 1515 and add up to 88. The numbers 33 and 55 satisfy these conditions because 3×5=153 \times 5 = 15 and 3+5=83 + 5 = 8.
  3. Write Factored Form: Write the factored form of the equation.\newlineThe equation can be factored as (j+3)(j+5)=0(j + 3)(j + 5) = 0.
  4. Solve Using Zero Product Property: Solve for jj using the zero product property.\newlineIf (j+3)(j+5)=0(j + 3)(j + 5) = 0, then either j+3=0j + 3 = 0 or j+5=0j + 5 = 0.\newlineFirst, solve j+3=0j + 3 = 0:\newlinej+3−3=0−3j + 3 - 3 = 0 - 3\newlinej=−3j = -3\newlineNext, solve j+5=0j + 5 = 0:\newlinej+5−5=0−5j + 5 - 5 = 0 - 5\newlinej=−5j = -5
  5. Write Solutions: Write the solutions for the equation j2+8j+15=0j^2 + 8j + 15 = 0. The solutions are j=−3j = -3 and j=−5j = -5.

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