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Solve using the quadratic formula.\newline2f2−9f+5=02f^2 - 9f + 5 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinef=f = _____ or f=f = _____

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Q. Solve using the quadratic formula.\newline2f2−9f+5=02f^2 - 9f + 5 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinef=f = _____ or f=f = _____
  1. Identify values: Identify the values of aa, bb, and cc in the quadratic equation 2f2−9f+5=02f^2 − 9f + 5 = 0. The quadratic equation is in the form af2+bf+c=0af^2 + bf + c = 0. For our equation, a=2a = 2, b=−9b = -9, and c=5c = 5.
  2. Substitute formula: Substitute the values of aa, bb, and cc into the quadratic formula f=−b±b2−4ac2af = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\newlineHere, f=−(−9)±(−9)2−4⋅2⋅52⋅2f = \frac{-(-9) \pm \sqrt{(-9)^2 - 4\cdot2\cdot5}}{2\cdot2}.
  3. Simplify terms: Simplify the terms inside the square root and the constants outside the square root.\newlinef=9±81−404f = \frac{9 \pm \sqrt{81 - 40}}{4}.\newlinef=9±414f = \frac{9 \pm \sqrt{41}}{4}.
  4. Calculate square root: Calculate the square root of 4141 to determine the two possible values for ff.41\sqrt{41} is an irrational number, so we will use it as is for the exact solution and then approximate it for the decimal solution.
  5. Write possible solutions: Write the two possible solutions for ff.f=9+414f = \frac{9 + \sqrt{41}}{4} or f=9−414f = \frac{9 - \sqrt{41}}{4}.
  6. Round values: If necessary, round the values of ff to the nearest hundredth.f≈(9+6.40)/4f \approx (9 + 6.40) / 4 or f≈(9−6.40)/4f \approx (9 - 6.40) / 4.f≈15.40/4f \approx 15.40 / 4 or f≈2.60/4f \approx 2.60 / 4.f≈3.85f \approx 3.85 or f≈0.65f \approx 0.65.

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