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Solve using the quadratic formula.\newline2y2+8y−2=02y^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.\newline2y2+8y−2=02y^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 coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation 2y2+8y−2=02y^2 + 8y - 2 = 0. Comparing 2y2+8y−2=02y^2 + 8y - 2 = 0 with the standard form ax2+bx+c=0ax^2 + bx + c = 0, we find: a=2a = 2 b=8b = 8 c=−2c = -2
  2. Substitute values into formula: Substitute the values of aa, bb, and cc into the quadratic formula y=−b±b2−4ac2ay = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\newlineThe quadratic formula is y=−8±82−4⋅2⋅(−2)2⋅2y = \frac{-8 \pm \sqrt{8^2 - 4\cdot2\cdot(-2)}}{2\cdot2}.
  3. Calculate discriminant: Calculate the discriminant part of the formula: b2−4acb^2 - 4ac. The discriminant is 82−4×2×(−2)=64+16=808^2 - 4\times2\times(-2) = 64 + 16 = 80.
  4. Calculate square root: Calculate the square root of the discriminant: 80\sqrt{80}. The square root of 8080 simplifies to 16×5\sqrt{16\times 5} which is 4×54\times\sqrt{5}.
  5. Substitute back into formula: Substitute the square root of the discriminant back into the quadratic formula.\newlineWe have y=−8±454y = \frac{-8 \pm 4\sqrt{5}}{4}.
  6. Simplify expression: Simplify the expression by dividing all terms by 44. This gives us y=(−2±5)y = (-2 \pm \sqrt{5}).
  7. Calculate possible solutions: Calculate the two possible solutions for yy. The first solution is y=−2+5y = -2 + \sqrt{5}. The second solution is y=−2−5y = -2 - \sqrt{5}.
  8. Round values if required: Round the values of yy to the nearest hundredth, if required.\newlineThe first solution is y≈−2+2.24y \approx -2 + 2.24 which is approximately 0.240.24.\newlineThe second solution is y≈−2−2.24y \approx -2 - 2.24 which is approximately −4.24-4.24.

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