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Solve using the quadratic formula.\newline2f2−8f+7=02f^2 - 8f + 7 = 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.\newline2f2−8f+7=02f^2 - 8f + 7 = 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 2f2−8f+7=02f^2 − 8f + 7 = 0. The quadratic equation is in the form af2+bf+c=0af^2 + bf + c = 0, so by comparing: a=2a = 2 b=−8b = -8 c=7c = 7
  2. Substitute values: 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}.\newlineSubstituting the values we get:\newlinef=−(−8)±(−8)2−4⋅2⋅72⋅2f = \frac{-(-8) \pm \sqrt{(-8)^2 - 4\cdot 2\cdot 7}}{2\cdot 2}
  3. Simplify equation: Simplify the equation.\newlinef=8±64−564f = \frac{8 \pm \sqrt{64 - 56}}{4}\newlinef=8±84f = \frac{8 \pm \sqrt{8}}{4}\newlineSince 8\sqrt{8} simplifies to 222\sqrt{2}, we can write:\newlinef=8±224f = \frac{8 \pm 2\sqrt{2}}{4}
  4. Divide terms: Simplify further by dividing the terms by 44.\newlinef=84±224f = \frac{8}{4} \pm \frac{2\sqrt{2}}{4}\newlinef=2±22f = 2 \pm \frac{\sqrt{2}}{2}
  5. Write solutions: Write the final solutions.\newlineThe two possible values for ff are:\newlinef=2+(2/2)f = 2 + (\sqrt{2}/2) or f=2−(2/2)f = 2 - (\sqrt{2}/2)\newlineTo round to the nearest hundredth:\newlinef≈2+0.71f \approx 2 + 0.71 or f≈2−0.71f \approx 2 - 0.71\newlinef≈2.71f \approx 2.71 or f≈1.29f \approx 1.29

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