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Solve using the quadratic formula.\newline7f2−8f+2=07f^2 - 8f + 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.\newline7f2−8f+2=07f^2 - 8f + 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 7f2−8f+2=07f^2 − 8f + 2 = 0. The quadratic equation is in the form af2+bf+c=0af^2 + bf + c = 0. Comparing this with our equation, we get: a=7a = 7 b=−8b = -8 c=2c = 2
  2. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula to find ff. The quadratic formula is f=−b±b2−4ac2af = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substituting the values we get: f=−(−8)±(−8)2−4⋅7⋅22⋅7f = \frac{-(-8) \pm \sqrt{(-8)^2 - 4\cdot7\cdot2}}{2\cdot7} f=8±64−5614f = \frac{8 \pm \sqrt{64 - 56}}{14}
  3. Simplify expression and fraction: Simplify the expression under the square root and the fraction. 64−56=8\sqrt{64 - 56} = \sqrt{8} So, we have: f=8±814f = \frac{8 \pm \sqrt{8}}{14}
  4. Simplify 8\sqrt{8}: Simplify 8\sqrt{8} and express it in simplest radical form.8=4⋅2=2⋅2\sqrt{8} = \sqrt{4\cdot2} = 2\cdot\sqrt{2} Now we can write the solutions for ff as: f=8±2⋅214f = \frac{8 \pm 2\cdot\sqrt{2}}{14}
  5. Simplify fractions: Simplify the fractions. \newlinef=4±27f = \frac{4 \pm \sqrt{2}}{7}\newlineThese are the solutions in their simplest form. If we need to express them as decimals rounded to the nearest hundredth, we calculate:\newlinef≈4+1.417f \approx \frac{4 + 1.41}{7} or f≈4−1.417f \approx \frac{4 - 1.41}{7}\newlinef≈5.417f \approx \frac{5.41}{7} or f≈2.597f \approx \frac{2.59}{7}\newlinef≈0.77f \approx 0.77 or f≈0.37f \approx 0.37

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