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Solve using the quadratic formula.\newline5f2−9f−2=05f^2 - 9f - 2 = 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.\newline5f2−9f−2=05f^2 - 9f - 2 = 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 5f2−9f−2=05f^2 − 9f − 2 = 0. The quadratic equation is in the form af2+bf+c=0af^2 + bf + c = 0, so by comparison: a=5a = 5 b=−9b = -9 c=−2c = -2
  2. Substitute into 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⋅5⋅(−2)2⋅5f = \frac{-(-9) \pm \sqrt{(-9)^2 - 4\cdot 5\cdot (-2)}}{2\cdot 5}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant). (−9)2−4⋅5⋅(−2)=81+40=121\sqrt{(-9)^2 - 4 \cdot 5 \cdot (-2)} = \sqrt{81 + 40} = \sqrt{121}
  4. Continue formula simplification: Continue simplifying the quadratic formula with the discriminant value.\newlinef=9±12110f = \frac{9 \pm \sqrt{121}}{10}\newlineSince 121=11\sqrt{121} = 11, we have:\newlinef=9±1110f = \frac{9 \pm 11}{10}
  5. Find possible values: Find the two possible values for ff.f=9+1110f = \frac{9 + 11}{10} or f=9−1110f = \frac{9 - 11}{10}f=2010f = \frac{20}{10} or f=−210f = \frac{-2}{10}f=2f = 2 or f=−15f = -\frac{1}{5}
  6. Check rounding necessity: Check if the solutions need to be rounded to the nearest hundredth.\newlineSince both solutions are already in the form of integers or proper fractions, no rounding is necessary.

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