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Solve using the quadratic formula.\newline4s2−9s−8=04s^2 - 9s - 8 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlines=s = _____ or s=s = _____

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Q. Solve using the quadratic formula.\newline4s2−9s−8=04s^2 - 9s - 8 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlines=s = _____ or s=s = _____
  1. Identify values of aa, bb, cc: Identify the values of aa, bb, and cc in the quadratic equation 4s2−9s−8=04s^2 − 9s − 8 = 0. Compare 4s2−9s−8=04s^2 − 9s − 8 = 0 with the standard form ax2+bx+c=0ax^2 + bx + c = 0. a=4a = 4 bb00 bb11
  2. Substitute values into formula: Substitute the values of aa, bb, and cc into the quadratic formula s=−b±b2−4ac2as = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\newlineSubstitute a=4a = 4, b=−9b = -9, and c=−8c = -8 into the quadratic formula.\newlines=−(−9)±(−9)2−4⋅4⋅(−8)2⋅4s = \frac{-(-9) \pm \sqrt{(-9)^2 - 4\cdot4\cdot(-8)}}{2\cdot4}\newlines=9±81+1288s = \frac{9 \pm \sqrt{81 + 128}}{8}
  3. Simplify expression and calculate discriminant: Simplify the expression under the square root and calculate the discriminant.\newline(−9)2−4⋅4⋅(−8)\sqrt{(-9)^2 - 4\cdot4\cdot(-8)}\newline= 81+128\sqrt{81 + 128}\newline= 209\sqrt{209}
  4. Calculate two possible solutions: Calculate the two possible solutions for ss.s=9±2098s = \frac{9 \pm \sqrt{209}}{8}We have two solutions:s=9+2098s = \frac{9 + \sqrt{209}}{8} and s=9−2098s = \frac{9 - \sqrt{209}}{8}
  5. Simplify solutions and round: Simplify the solutions and, if necessary, round to the nearest hundredth.\newlineFirst solution:\newlines=9+2098s = \frac{9 + \sqrt{209}}{8}\newlineSecond solution:\newlines=9−2098s = \frac{9 - \sqrt{209}}{8}\newlineIf we need to round to the nearest hundredth, we can use a calculator to find the approximate decimal values.
  6. Approximate decimal values: Use a calculator to approximate the decimal values of ss. First solution: s≈(9+14.456)/8s \approx (9 + 14.456) / 8 s≈23.456/8s \approx 23.456 / 8 s≈2.932s \approx 2.932 Second solution: s≈(9−14.456)/8s \approx (9 - 14.456) / 8 s≈−5.456/8s \approx -5.456 / 8 s≈−0.682s \approx -0.682

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