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Solve for qq. \newlineq2+22q+121=0q^2 + 22q + 121 = 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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Full solution

Q. Solve for qq. \newlineq2+22q+121=0q^2 + 22q + 121 = 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. Factor Quadratic Equation: Factor the quadratic equation q2+22q+121q^2 + 22q + 121. Notice that 121121 is a perfect square, and 2222 is twice the square root of 121121, which is 1111. So, (q+11)(q+11)=q2+22q+121(q + 11)(q + 11) = q^2 + 22q + 121.
  2. Set Factors Equal: Set each factor equal to zero: (q+11)=0(q + 11) = 0.
  3. Solve for q: Solve for qq: q+11=0q + 11 = 0.\newlineSubtract 1111 from both sides to get q=−11q = -11.

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