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Solve for dd.\newlined2+7d+12=0d^2 + 7d + 12 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlined=d = ____

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Q. Solve for dd.\newlined2+7d+12=0d^2 + 7d + 12 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlined=d = ____
  1. Identify Equation: Identify the quadratic equation to be solved.\newlineThe given quadratic equation is d2+7d+12=0d^2 + 7d + 12 = 0.
  2. Factor Equation: Factor the quadratic equation.\newlineWe need to find two numbers that multiply to 1212 and add up to 77. The numbers 33 and 44 satisfy these conditions because 3×4=123 \times 4 = 12 and 3+4=73 + 4 = 7.
  3. Write Factored Form: Write the equation in its factored form.\newlineThe factored form of the equation is (d+3)(d+4)=0(d + 3)(d + 4) = 0.
  4. Set Equal and Solve: Set each factor equal to zero and solve for dd.\newlineFirst, set d+3=0d + 3 = 0 and solve for dd.\newlineSubtract 33 from both sides to get d=−3d = -3.
  5. Solve First Factor: Solve the second factor.\newlineNow, set d+4=0d + 4 = 0 and solve for dd.\newlineSubtract 44 from both sides to get d=−4d = -4.
  6. Write Solutions: Write the solutions for the equation d2+7d+12=0d^2 + 7d + 12 = 0. The solutions are d=−3d = -3 and d=−4d = -4.

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