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Solve for qq.\newlineq2+13q−14=0q^2 + 13q - 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.\newlineq = ____

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Solve a quadratic equation by factoringright chevron icon

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Q. Solve for qq.\newlineq2+13q−14=0q^2 + 13q - 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.\newlineq = ____
  1. Identify Quadratic Equation: Identify the quadratic equation to be solved.\newlineThe given quadratic equation is q2+13q−14=0q^2 + 13q - 14 = 0. We need to find values of qq that satisfy this equation.
  2. Factor Equation: Factor the quadratic equation.\newlineWe need to find two numbers that multiply to −14-14 and add up to 1313. The numbers 1414 and −1-1 satisfy these conditions because 14×(−1)=−1414 \times (-1) = -14 and 14+(−1)=1314 + (-1) = 13.
  3. Write Factored Form: Write the factored form of the equation.\newlineThe equation q2+13q−14=0q^2 + 13q - 14 = 0 can be factored as (q+14)(q−1)=0(q + 14)(q - 1) = 0.
  4. Solve Using Zero Product Property: Solve for qq using the zero product property.\newlineIf (q+14)(q−1)=0(q + 14)(q - 1) = 0, then either q+14=0q + 14 = 0 or q−1=0q - 1 = 0.
  5. Solve First Equation: Solve the first equation q+14=0q + 14 = 0.\newlineSubtract 1414 from both sides to isolate qq.\newlineq+14−14=0−14q + 14 - 14 = 0 - 14\newlineq=−14q = -14
  6. Solve Second Equation: Solve the second equation q−1=0q - 1 = 0. Add 11 to both sides to isolate qq. q−1+1=0+1q - 1 + 1 = 0 + 1 q=1q = 1

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