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Solve using the quadratic formula.\newline2d2+4d+1=02d^2 + 4d + 1 = 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+4d+1=02d^2 + 4d + 1 = 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+4d+1=02d^2 + 4d + 1 = 0. By comparing the equation to the standard form ax2+bx+c=0ax^2 + bx + c = 0, we find: a=2a = 2 b=4b = 4 c=1c = 1
  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=−(4)±(4)2−4⋅2⋅12⋅2d = \frac{-(4) \pm \sqrt{(4)^2 - 4\cdot2\cdot1}}{2\cdot2}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant). (4)2−4⋅2⋅1=16−8=8\sqrt{(4)^2 - 4\cdot 2\cdot 1} = \sqrt{16 - 8} = \sqrt{8}
  4. Simplify formula: Simplify the quadratic formula with the values we have.\newlined=−4±84d = \frac{-4 \pm \sqrt{8}}{4}\newlineSince 8\sqrt{8} can be simplified to 222\sqrt{2}, we can rewrite the equation as:\newlined=−4±224d = \frac{-4 \pm 2\sqrt{2}}{4}
  5. Divide by 44: Simplify the equation further by dividing both terms in the numerator by 44.d=(−1±(12)2)d = (-1 \pm (\frac{1}{2})\sqrt{2})
  6. Round values: If necessary, round the values of dd to the nearest hundredth. The decimal approximation of 2\sqrt{2} is about 1.411.41. So we have: d=−1+(1/2)×1.41d = -1 + (1/2)\times1.41 or d=−1−(1/2)×1.41d = -1 - (1/2)\times1.41 d≈−1+0.705d \approx -1 + 0.705 or d≈−1−0.705d \approx -1 - 0.705 d≈−0.295d \approx -0.295 or d≈−1.705d \approx -1.705

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