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Solve for qq.\newlineq2+9q+18=0q^2 + 9q + 18 = 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+9q+18=0q^2 + 9q + 18 = 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+9q+18=0q^2 + 9q + 18 = 0. We need to find two numbers that multiply to give 1818 and add up to give 99.
  2. Factor equation: Factor the quadratic equation.\newlineThe two numbers that multiply to 1818 and add up to 99 are 33 and 66, since 3×6=183 \times 6 = 18 and 3+6=93 + 6 = 9.\newlineTherefore, we can write the equation as (q+3)(q+6)=0(q + 3)(q + 6) = 0.
  3. Solve using zero product property: Solve for qq using the zero product property.\newlineIf (q+3)(q+6)=0(q + 3)(q + 6) = 0, then either q+3=0q + 3 = 0 or q+6=0q + 6 = 0.
  4. Solve first equation: Solve the first equation q+3=0q + 3 = 0.\newlineSubtract 33 from both sides to isolate qq.\newlineq+3−3=0−3q + 3 - 3 = 0 - 3\newlineq=−3q = -3
  5. Solve second equation: Solve the second equation q+6=0q + 6 = 0.\newlineSubtract 66 from both sides to isolate qq.\newlineq+6−6=0−6q + 6 - 6 = 0 - 6\newlineq=−6q = -6

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