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Solve using the quadratic formula.\newline7d2+d−2=07d^2 + d - 2 = 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.\newline7d2+d−2=07d^2 + d - 2 = 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 7d2+d−2=07d^2 + d - 2 = 0. The quadratic equation is in the form ad2+bd+c=0ad^2 + bd + c = 0, so by comparing: a=7a = 7 b=1b = 1 c=−2c = -2
  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=−(1)±(1)2−4⋅7⋅(−2)2⋅7d = \frac{-(1) \pm \sqrt{(1)^2 - 4\cdot7\cdot(-2)}}{2\cdot7}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant). (1)2−4⋅7⋅(−2)=1+56=57\sqrt{(1)^2 - 4 \cdot 7 \cdot (-2)} = \sqrt{1 + 56} = \sqrt{57}
  4. Continue with formula: Continue simplifying the quadratic formula with the values found.\newlined=−1±5714d = \frac{-1 \pm \sqrt{57}}{14}\newlineThis gives us two possible solutions for dd:\newlined=−1+5714d = \frac{-1 + \sqrt{57}}{14} or d=−1−5714d = \frac{-1 - \sqrt{57}}{14}
  5. Calculate decimal values: Calculate the approximate decimal values of dd, if necessary, rounding to the nearest hundredth.d≈(−1+7.55)14d \approx \frac{{(-1 + 7.55)}}{{14}} or d≈(−1−7.55)14d \approx \frac{{(-1 - 7.55)}}{{14}}d≈6.5514d \approx \frac{{6.55}}{{14}} or d≈−8.5514d \approx \frac{{-8.55}}{{14}}d≈0.47d \approx 0.47 or d≈−0.61d \approx -0.61

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