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Solve for dd. \newlined2−10d−24=0d^2 - 10d - 24 = 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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Solve a quadratic equation by factoringright chevron icon

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Q. Solve for dd. \newlined2−10d−24=0d^2 - 10d - 24 = 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 the quadratic equation: Identify the quadratic equation to be solved.\newlineThe given quadratic equation is d2−10d−24=0d^2 - 10d - 24 = 0. We need to find values of dd that satisfy this equation.
  2. Factor the quadratic equation: Factor the quadratic equation.\newlineWe need to find two numbers that multiply to −24-24 and add up to −10-10. The numbers −12-12 and 22 satisfy these conditions because −12×2=−24-12 \times 2 = -24 and −12+2=−10-12 + 2 = -10.
  3. Write factored form: Write the factored form of the equation.\newlineUsing the numbers found in Step 22, we can write the factored form of the equation as (d−12)(d+2)=0(d - 12)(d + 2) = 0.
  4. Solve using zero product property: Solve for dd using the zero product property.\newlineIf (d−12)(d+2)=0(d - 12)(d + 2) = 0, then either d−12=0d - 12 = 0 or d+2=0d + 2 = 0.\newlineFirst, solve d−12=0d - 12 = 0:\newlineAdd 1212 to both sides to get d=12d = 12.\newlineSecond, solve d+2=0d + 2 = 0:\newlineSubtract 22 from both sides to get d=−2d = -2.

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