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Solve using the quadratic formula.\newline2d2+9d−5=02d^2 + 9d - 5 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlined=d = _____ or d=d = _____

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Q. Solve using the quadratic formula.\newline2d2+9d−5=02d^2 + 9d - 5 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlined=d = _____ or d=d = _____
  1. Identify values: Identify values of aa, bb, and cc from the equation 2d2+9d−5=02d^2 + 9d - 5 = 0. Here, a=2a = 2, b=9b = 9, and c=−5c = -5.
  2. Plug into quadratic formula: Plug aa, bb, and cc into the quadratic formula: d=−b±b2−4ac2ad = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. So, d=−(9)±(9)2−4(2)(−5)2(2)d = \frac{-(9) \pm \sqrt{(9)^2 - 4(2)(-5)}}{2(2)}.
  3. Simplify square root: Simplify inside the square root: (9)2−4(2)(−5)=81+40=121\sqrt{(9)^2 - 4(2)(-5)} = \sqrt{81 + 40} = \sqrt{121}.
  4. Calculate square root: Calculate the square root: 121=11\sqrt{121} = 11.
  5. Substitute back into formula: Now, substitute the square root back into the formula: d=−9±114d = \frac{{-9 \pm 11}}{{4}}.
  6. Find possible solutions: Find the two possible solutions for dd: d=−9+114d = \frac{{-9 + 11}}{{4}} or d=−9−114d = \frac{{-9 - 11}}{{4}}.
  7. Simplify both solutions: Simplify both solutions: d=24d = \frac{2}{4} or d=−204d = \frac{-20}{4}.
  8. Reduce to simplest form: Reduce the fractions to simplest form: d=12d = \frac{1}{2} or d=−5d = -5.
  9. Round non-integer solution: Round the non-integer solution to the nearest hundredth if necessary: d=0.50d = 0.50 or d=−5d = -5.

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