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Solve for qq.\newlineq2−6q−7=0q^2 - 6q - 7 = 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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Q. Solve for qq.\newlineq2−6q−7=0q^2 - 6q - 7 = 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 Equation: Identify the quadratic equation to be solved.\newlineThe given quadratic equation is q2−6q−7=0q^2 - 6q - 7 = 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 −7-7 and add up to −6-6. The numbers −7-7 and 11 satisfy these conditions because −7×1=−7-7 \times 1 = -7 and −7+1=−6-7 + 1 = -6.\newlineSo we can write the equation as (q−7)(q+1)=0(q - 7)(q + 1) = 0.
  3. Solve Using Property: Solve for qq using the zero product property.\newlineIf (q−7)(q+1)=0(q - 7)(q + 1) = 0, then either q−7=0q - 7 = 0 or q+1=0q + 1 = 0.\newlineFor q−7=0q - 7 = 0:\newlineq=7q = 7\newlineFor q+1=0q + 1 = 0:\newlineq=−1q = -1\newlineWe have found the two solutions for qq.

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