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Solve using the quadratic formula.\newline2y2+8y−7=02y^2 + 8y - 7 = 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.\newline2y2+8y−7=02y^2 + 8y - 7 = 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 values of aa, bb, and cc from the equation 2y2+8y−7=02y^2 + 8y - 7 = 0; a=2a=2, b=8b=8, c=−7c=-7.
  2. Plug into formula: Plug aa, bb, and cc into the quadratic formula y=−b±b2−4ac2ay = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Calculate discriminant: Calculate the discriminant: b2−4ac=82−4⋅2⋅(−7)\sqrt{b^2 - 4ac} = \sqrt{8^2 - 4\cdot 2\cdot (-7)}.
  4. Perform calculation: Perform the calculation: 64+56=120.\sqrt{64 + 56} = \sqrt{120}.
  5. Write solutions: Write down the two possible solutions for yy: y=−8±1202×2y = \frac{-8 \pm \sqrt{120}}{2 \times 2}.
  6. Simplify solutions: Simplify the solutions: y=−8±1204y = \frac{{-8 \pm \sqrt{120}}}{4}.
  7. Calculate decimal values: Calculate the approximate decimal values: y≈(−8+10.95)/4y \approx (-8 + 10.95) / 4 or y≈(−8−10.95)/4y \approx (-8 - 10.95) / 4.
  8. Finish calculation: Finish the calculation: y≈2.954y \approx \frac{2.95}{4} or y≈−18.954y \approx \frac{-18.95}{4}.
  9. Round to nearest hundredth: Round to the nearest hundredth: y≈0.74y \approx 0.74 or y≈−4.74y \approx -4.74.

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