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Solve using the quadratic formula.\newline2d2+8d+5=02d^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.\newline2d2+8d+5=02d^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 values: Identify the values of aa, bb, and cc in the quadratic equation 2d2+8d+5=02d^2 + 8d + 5 = 0. By comparing the equation to the standard form ax2+bx+c=0ax^2 + bx + c = 0, we find: a=2a = 2 b=8b = 8 c=5c = 5
  2. Substitute in formula: 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⋅2⋅52⋅2d = \frac{-(8) \pm \sqrt{(8)^2 - 4\cdot2\cdot5}}{2\cdot2}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant). (8)2−4⋅2⋅5=64−40=24\sqrt{(8)^2 - 4\cdot 2\cdot 5} = \sqrt{64 - 40} = \sqrt{24}
  4. Continue simplifying: Continue simplifying the quadratic formula with the values we have. d=−8±244d = \frac{{-8 \pm \sqrt{24}}}{{4}}
  5. Simplify radical form: Simplify 24\sqrt{24} to its simplest radical form. 24\sqrt{24} can be simplified to 262\sqrt{6} because 24=4×624 = 4\times 6 and 4=2\sqrt{4} = 2. So we have: d=−8±264d = \frac{-8 \pm 2\sqrt{6}}{4}
  6. Divide by common factor: Simplify the expression by dividing all terms by the common factor of 22.d=−4±62d = \frac{-4 \pm \sqrt{6}}{2}
  7. Identify possible values: Identify the two possible values for dd.d=−4+62d = \frac{{-4 + \sqrt{6}}}{{2}} or d=−4−62d = \frac{{-4 - \sqrt{6}}}{{2}}
  8. Round to nearest hundredth: Round the values of dd to the nearest hundredth, if necessary.d≈(−4+2.45)/2d \approx (-4 + 2.45) / 2 or d≈(−4−2.45)/2d \approx (-4 - 2.45) / 2d≈−1.55/2d \approx -1.55 / 2 or d≈−6.45/2d \approx -6.45 / 2d≈−0.775d \approx -0.775 or d≈−3.225d \approx -3.225

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