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Solve using the quadratic formula.\newline5d2+8d+3=05d^2 + 8d + 3 = 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.\newline5d2+8d+3=05d^2 + 8d + 3 = 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 the values of aa, bb, and cc in the quadratic equation 5d2+8d+3=05d^2 + 8d + 3 = 0. The quadratic equation is in the form ad2+bd+c=0ad^2 + bd + c = 0, so by comparison: a=5a = 5 b=8b = 8 c=3c = 3
  2. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula to find dd. The quadratic formula is d=−b±b2−4ac2ad = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. So we have: d=−(8)±(8)2−4⋅5⋅32⋅5d = \frac{-(8) \pm \sqrt{(8)^2 - 4\cdot 5\cdot 3}}{2\cdot 5}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant). (8)2−4⋅5⋅3=64−60=4\sqrt{(8)^2 - 4\cdot 5\cdot 3} = \sqrt{64 - 60} = \sqrt{4}
  4. Continue simplifying: Continue simplifying the quadratic formula with the values found.\newlined=−8±410d = \frac{-8 \pm \sqrt{4}}{10}\newlineSince 4=2\sqrt{4} = 2, we have:\newlined=−8±210d = \frac{-8 \pm 2}{10}
  5. Find possible values: Find the two possible values for dd.\newlineFirst solution:\newlined=(−8+2)/10=−6/10=−3/5d = (-8 + 2) / 10 = -6 / 10 = -3 / 5\newlineSecond solution:\newlined=(−8−2)/10=−10/10=−1d = (-8 - 2) / 10 = -10 / 10 = -1
  6. Simplify solutions: Simplify the solutions and, if necessary, round to the nearest hundredth.\newlineThe first solution is already in simplest form as a fraction:\newlined=−35d = -\frac{3}{5}\newlineThe second solution is an integer:\newlined=−1d = -1\newlineNo rounding is necessary as both solutions are exact.

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