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Solve using the quadratic formula.\newline6d2−4d−4=06d^2 - 4d - 4 = 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.\newline6d2−4d−4=06d^2 - 4d - 4 = 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 6d2−4d−4=06d^2 − 4d − 4 = 0. The quadratic equation is in the form ad2+bd+c=0ad^2 + bd + c = 0, so by comparison: a=6a = 6 b=−4b = -4 c=−4c = -4
  2. Substitute into 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=−(−4)±(−4)2−4⋅6⋅(−4)2⋅6d = \frac{-(-4) \pm \sqrt{(-4)^2 - 4\cdot6\cdot(-4)}}{2\cdot6}
  3. Simplify terms: Simplify the terms inside the square root and the constants outside the square root. \newlined=4±16+9612d = \frac{4 \pm \sqrt{16 + 96}}{12}\newlined=4±11212d = \frac{4 \pm \sqrt{112}}{12}
  4. Simplify square root: Simplify the square root. 112\sqrt{112} can be simplified to 16×7\sqrt{16\times7}, which is 4×74\times\sqrt{7}. So we have: d=4±4×712d = \frac{4 \pm 4\times\sqrt{7}}{12}
  5. Divide by common factor: Simplify the expression by dividing all terms by the common factor of 44. \newlined=1±73d = \frac{1 \pm \sqrt{7}}{3}
  6. Identify possible values: Identify the two possible values for dd.d=1+73d = \frac{1 + \sqrt{7}}{3} or d=1−73d = \frac{1 - \sqrt{7}}{3}
  7. Round to nearest hundredth: Round the values of dd to the nearest hundredth, if necessary.d=1+73d = \frac{1 + \sqrt{7}}{3} or d=1−73d = \frac{1 - \sqrt{7}}{3}d≈1+2.653d \approx \frac{1 + 2.65}{3} or d≈1−2.653d \approx \frac{1 - 2.65}{3}d≈3.653d \approx \frac{3.65}{3} or d≈−1.653d \approx \frac{-1.65}{3}d≈1.22d \approx 1.22 or d≈−0.55d \approx -0.55

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