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Solve using the quadratic formula.\newline5y28y+2=05y^2 - 8y + 2 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliney=y = _____ or y=y = _____

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Q. Solve using the quadratic formula.\newline5y28y+2=05y^2 - 8y + 2 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliney=y = _____ or y=y = _____
  1. Identify values: Identify the values of aa, bb, and cc in the quadratic equation 5y28y+2=05y^2 − 8y + 2 = 0. The quadratic equation is in the form ay2+by+c=0ay^2 + by + c = 0. For our equation, a=5a = 5, b=8b = -8, and c=2c = 2.
  2. Substitute in formula: Substitute the values of aa, bb, and cc into the quadratic formula y=b±b24ac2ay = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substitute a=5a = 5, b=8b = -8, and c=2c = 2 into the formula. y=(8)±(8)245225y = \frac{-(-8) \pm \sqrt{(-8)^2 - 4\cdot 5\cdot 2}}{2\cdot 5} y=8±644010y = \frac{8 \pm \sqrt{64 - 40}}{10}
  3. Simplify and calculate discriminant: Simplify the expression under the square root and calculate the discriminant. 6440=24\sqrt{64 - 40} = \sqrt{24} The discriminant is 2424, which is positive, indicating that we will have two real solutions.
  4. Continue simplifying formula: Continue simplifying the quadratic formula with the calculated discriminant.\newliney=8±2410y = \frac{8 \pm \sqrt{24}}{10}\newliney=8±2610y = \frac{8 \pm 2\sqrt{6}}{10}\newliney=4±65y = \frac{4 \pm \sqrt{6}}{5}
  5. Write possible solutions: Write the two possible solutions for yy.y=4+65y = \frac{4 + \sqrt{6}}{5} or y=465y = \frac{4 - \sqrt{6}}{5}
  6. Round if necessary: If necessary, round the values of yy to the nearest hundredth.y(4+2.45)/5y \approx (4 + 2.45) / 5 or y(42.45)/5y \approx (4 - 2.45) / 5y6.45/5y \approx 6.45 / 5 or y1.55/5y \approx 1.55 / 5y1.29y \approx 1.29 or y0.31y \approx 0.31

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