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Solve using the quadratic formula.\newline9d2+7d−5=09d^2 + 7d - 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.\newline9d2+7d−5=09d^2 + 7d - 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 from the quadratic equation 9d2+7d−5=09d^2 + 7d - 5 = 0. Compare 9d2+7d−5=09d^2 + 7d - 5 = 0 with the standard form ax2+bx+c=0ax^2 + bx + c = 0. a=9a = 9 b=7b = 7 c=−5c = -5
  2. Substitute 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}. Substitute a=9a = 9, b=7b = 7, and c=−5c = -5 into the quadratic formula. d=−(7)±(7)2−4⋅9⋅(−5)2⋅9d = \frac{-(7) \pm \sqrt{(7)^2 - 4\cdot9\cdot(-5)}}{2\cdot9}
  3. Simplify and calculate: Simplify the expression under the square root and calculate its value.\newline(7)2−4⋅9⋅(−5)\sqrt{(7)^2 - 4\cdot 9\cdot (-5)}\newline= 49+180\sqrt{49 + 180}\newline= 229\sqrt{229}
  4. Calculate solutions: Calculate the two possible solutions for dd.d=−7±2292⋅9d = \frac{-7 \pm \sqrt{229}}{2 \cdot 9}d=−7±22918d = \frac{-7 \pm \sqrt{229}}{18}d=−7+22918d = \frac{-7 + \sqrt{229}}{18} or d=−7−22918d = \frac{-7 - \sqrt{229}}{18}
  5. Round to nearest hundredth: Round the values of dd to the nearest hundredth, if required.d=−7+22918d = \frac{{-7 + \sqrt{229}}}{{18}} or d=−7−22918d = \frac{{-7 - \sqrt{229}}}{{18}}d≈−7+15.1318d \approx \frac{{-7 + 15.13}}{{18}} or d≈−7−15.1318d \approx \frac{{-7 - 15.13}}{{18}}d≈8.1318d \approx \frac{{8.13}}{{18}} or d≈−22.1318d \approx \frac{{-22.13}}{{18}}d≈0.45d \approx 0.45 or d≈−1.23d \approx -1.23

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