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Solve using the quadratic formula.\newline5y26y4=05y^2 - 6y - 4 = 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.\newline5y26y4=05y^2 - 6y - 4 = 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 5y26y4=05y^2 − 6y − 4 = 0. Comparing 5y26y4=05y^2 − 6y − 4 = 0 with the standard form ax2+bx+c=0ax^2 + bx + c = 0, we find: a=5a = 5 b=6b = -6 c=4c = -4
  2. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula y=b±b24ac2ay = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\newlineThe quadratic formula is y=(6)±(6)245(4)25y = \frac{-(-6) \pm \sqrt{(-6)^2 - 4\cdot5\cdot(-4)}}{2\cdot5}.
  3. Simplify expression: Simplify the expression inside the square root and the constants outside the square root.\newlineCalculate the discriminant: b24ac=(6)245(4)=36+80=116b^2 - 4ac = (-6)^2 - 4\cdot 5\cdot (-4) = 36 + 80 = 116.\newlineThen, the quadratic formula becomes y=6±11610y = \frac{6 \pm \sqrt{116}}{10}.
  4. Calculate solutions: Simplify the square root of 116116.\newlineSince 116116 is not a perfect square, we will leave it as 116\sqrt{116} for now.\newlineThe quadratic formula now is y=6±11610y = \frac{6 \pm \sqrt{116}}{10}.
  5. Round values: Calculate the two possible solutions for yy.\newlineFirst solution: y=6+11610y = \frac{6 + \sqrt{116}}{10}.\newlineSecond solution: y=611610y = \frac{6 - \sqrt{116}}{10}.
  6. Round values: Calculate the two possible solutions for yy. First solution: y=6+11610y = \frac{6 + \sqrt{116}}{10}. Second solution: y=611610y = \frac{6 - \sqrt{116}}{10}. Round the values of yy to the nearest hundredth, if required. First, we calculate the approximate values of 116\sqrt{116} which is approximately 10.7710.77. Then, we have y6+10.7710y \approx \frac{6 + 10.77}{10} or y610.7710y \approx \frac{6 - 10.77}{10}. y16.7710y \approx \frac{16.77}{10} or y4.7710y \approx \frac{-4.77}{10}. y=6+11610y = \frac{6 + \sqrt{116}}{10}00 or y=6+11610y = \frac{6 + \sqrt{116}}{10}11.

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