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Solve using the quadratic formula.\newline4f2−9f−4=04f^2 - 9f - 4 = 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.\newline4f2−9f−4=04f^2 - 9f - 4 = 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 4f2−9f−4=04f^2 − 9f − 4 = 0. The quadratic equation is in the form af2+bf+c=0af^2 + bf + c = 0. Comparing this with our equation, we get: a=4a = 4 b=−9b = -9 c=−4c = -4
  2. Substitute formula: Substitute the values of aa, bb, and cc into the quadratic formula.\newlineThe quadratic formula is f=−b±b2−4ac2af = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substituting the values we get:\newlinef=−(−9)±(−9)2−4⋅4⋅(−4)2⋅4f = \frac{-(-9) \pm \sqrt{(-9)^2 - 4\cdot4\cdot(-4)}}{2\cdot4}
  3. Simplify and calculate: Simplify the terms inside the square root and calculate the discriminant.\newlineThe discriminant is b2−4acb^2 - 4ac, so we have:\newlineDiscriminant = (−9)2−4⋅4⋅(−4)(-9)^2 - 4\cdot4\cdot(-4)\newlineDiscriminant = 81−(−64)81 - (-64)\newlineDiscriminant = 81+6481 + 64\newlineDiscriminant = 145145
  4. Continue with formula: Continue with the quadratic formula using the discriminant.\newlineNow we have:\newlinef=9±1458f = \frac{9 \pm \sqrt{145}}{8}
  5. Identify possible values: Identify the two possible values for ff. The two possible solutions are: f=9+1458f = \frac{9 + \sqrt{145}}{8} or f=9−1458f = \frac{9 - \sqrt{145}}{8}
  6. Simplify solutions: Simplify the solutions and, if necessary, round to the nearest hundredth.\newlineFirst solution:\newlinef=9+1458f = \frac{9 + \sqrt{145}}{8}\newlinef≈9+12.048f \approx \frac{9 + 12.04}{8}\newlinef≈21.048f \approx \frac{21.04}{8}\newlinef≈2.63f \approx 2.63\newlineSecond solution:\newlinef=9−1458f = \frac{9 - \sqrt{145}}{8}\newlinef≈9−12.048f \approx \frac{9 - 12.04}{8}\newlinef≈−3.048f \approx \frac{-3.04}{8}\newlinef≈−0.38f \approx -0.38

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