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Solve using the quadratic formula.\newline3d2+8d−5=03d^2 + 8d - 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.\newline3d2+8d−5=03d^2 + 8d - 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 coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation 3d2+8d−5=03d^2 + 8d - 5 = 0 by comparing it to the standard form ax2+bx+c=0ax^2 + bx + c = 0.a=3a = 3b=8b = 8c=−5c = -5
  2. Substitute values into formula: Substitute the values of aa, bb, and cc into the quadratic formula d=−b±b2−4ac2ad = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\newlined=−(8)±(8)2−4⋅3⋅(−5)2⋅3d = \frac{-(8) \pm \sqrt{(8)^2 - 4\cdot3\cdot(-5)}}{2\cdot3}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant). (8)2−4⋅3⋅(−5)=64+60=124\sqrt{(8)^2 - 4\cdot 3\cdot (-5)} = \sqrt{64 + 60} = \sqrt{124}
  4. Continue simplifying formula: Continue simplifying the quadratic formula with the calculated discriminant. d=−8±1246d = \frac{{-8 \pm \sqrt{124}}}{{6}}
  5. Simplify square root: Simplify the square root of 124124 to its simplest radical form if possible.124\sqrt{124} can be simplified to 2312\sqrt{31} because 124=4×31124 = 4\times31.d=−8±2316d = \frac{-8 \pm 2\sqrt{31}}{6}
  6. Divide by common factor: Simplify the expression by dividing all terms by the common factor of 22.d=(−4±313)d = (\frac{-4 \pm \sqrt{31}}{3})
  7. Identify possible solutions: Identify the two possible solutions for dd.d=−4+313d = \frac{-4 + \sqrt{31}}{3} or d=−4−313d = \frac{-4 - \sqrt{31}}{3}
  8. Round to nearest hundredth: Round the values of dd to the nearest hundredth, if necessary.d≈(−4+5.57)/3d \approx (-4 + 5.57) / 3 or d≈(−4−5.57)/3d \approx (-4 - 5.57) / 3d≈1.57/3d \approx 1.57 / 3 or d≈−9.57/3d \approx -9.57 / 3d≈0.52d \approx 0.52 or d≈−3.19d \approx -3.19

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