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Solve using the quadratic formula.\newline2n2−2n−9=02n^2 - 2n - 9 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinen=n = _____ or n=n = _____

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Q. Solve using the quadratic formula.\newline2n2−2n−9=02n^2 - 2n - 9 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinen=n = _____ or n=n = _____
  1. Plug Coefficients Quadratic Formula: Plug the coefficients into the quadratic formula n=−b±b2−4ac2an = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\newlinen=−(−2)±(−2)2−4⋅2⋅(−9)2⋅2n = \frac{-(-2) \pm \sqrt{(-2)^2 - 4\cdot 2 \cdot (-9)}}{2\cdot 2}.
  2. Simplify Equation: Simplify the equation.\newlinen=2±4+724n = \frac{2 \pm \sqrt{4 + 72}}{4}.\newlinen=2±764n = \frac{2 \pm \sqrt{76}}{4}.
  3. Calculate Solutions: Simplify 76\sqrt{76}.76\sqrt{76} is approximately 8.728.72.n=2±8.724n = \frac{2 \pm 8.72}{4}.
  4. Simplify 76\sqrt{76}: Calculate the two possible solutions for nn.\newlinen=(2+8.72)4n = \frac{(2 + 8.72)}{4} or n=(2−8.72)4n = \frac{(2 - 8.72)}{4}.\newlinen=10.724n = \frac{10.72}{4} or n=−6.724n = \frac{-6.72}{4}.
  5. Simplify Fractions: Simplify the fractions. n=2.68n = 2.68 or n=−1.68n = -1.68. Round to the nearest hundredth if needed.

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