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Solve for qq. \newlineq2+10q+16=0q^2 + 10q + 16 = 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=q = ____

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Solve a quadratic equation by factoringright chevron icon

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Q. Solve for qq. \newlineq2+10q+16=0q^2 + 10q + 16 = 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=q = ____
  1. Identify Equation: Identify the quadratic equation to be solved.\newlineWe have the quadratic equation q2+10q+16=0q^2 + 10q + 16 = 0.\newlineWe need to find two numbers that multiply to 1616 and add up to 1010.
  2. Factor Equation: Factor the quadratic equation.\newlineThe two numbers that multiply to 1616 and add up to 1010 are 22 and 88.\newlineSo we can write the equation as (q+2)(q+8)=0(q + 2)(q + 8) = 0.
  3. Solve Using Property: Solve for qq using the zero product property.\newlineIf (q+2)(q+8)=0(q + 2)(q + 8) = 0, then either q+2=0q + 2 = 0 or q+8=0q + 8 = 0.
  4. Solve First Equation: Solve the first equation q+2=0q + 2 = 0.\newlineSubtract 22 from both sides to get q=−2q = -2.
  5. Solve Second Equation: Solve the second equation q+8=0q + 8 = 0. Subtract 88 from both sides to get q=−8q = -8.
  6. Write Solutions: Write the solutions for the equation q2+10q+16=0q^2 + 10q + 16 = 0. The values of qq are −2-2 and −8-8.

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