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Solve using the quadratic formula.\newline2q2−4q−9=02q^2 - 4q - 9 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineq=q = _____ or q=q = _____

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Q. Solve using the quadratic formula.\newline2q2−4q−9=02q^2 - 4q - 9 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineq=q = _____ or q=q = _____
  1. Identify values of aa, bb, and cc: Identify values of aa, bb, and cc in the equation 2q2−4q−9=02q^2 − 4q − 9 = 0.a=2a = 2, b=−4b = -4, c=−9c = -9.
  2. Plug into quadratic formula: Plug aa, bb, and cc into the quadratic formula q=−b±b2−4ac2aq = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\newlineq=−(−4)±(−4)2−4⋅2⋅(−9)2⋅2q = \frac{-(-4) \pm \sqrt{(-4)^2 - 4\cdot2\cdot(-9)}}{2\cdot2}.
  3. Simplify and calculate: Simplify inside the square root and the constants outside.\newlineq=4±16+724q = \frac{4 \pm \sqrt{16 + 72}}{4}.\newlineq=4±884q = \frac{4 \pm \sqrt{88}}{4}.
  4. Simplify square root and reduce: Simplify the square root (if possible) and reduce the fraction.88\sqrt{88} simplifies to 2222\sqrt{22}.q=4±2224q = \frac{4 \pm 2\sqrt{22}}{4}.q=1±0.522q = 1 \pm 0.5\sqrt{22}.
  5. Calculate two possible solutions: Calculate the two possible solutions for qq.q=1+0.522q = 1 + 0.5\sqrt{22} or q=1−0.522q = 1 - 0.5\sqrt{22}.
  6. Round to nearest hundredth: Round the values of qq to the nearest hundredth, if required.q≈1+0.5×4.69q \approx 1 + 0.5 \times 4.69 or q≈1−0.5×4.69q \approx 1 - 0.5 \times 4.69.q≈1+2.345q \approx 1 + 2.345 or q≈1−2.345q \approx 1 - 2.345.q≈3.35q \approx 3.35 or q≈−1.35q \approx -1.35.

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