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Solve using the quadratic formula.\newline6s2−9s+3=06s^2 - 9s + 3 = 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.\newline6s2−9s+3=06s^2 - 9s + 3 = 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 6s2−9s+3=06s^2 − 9s + 3 = 0. The quadratic equation is in the form as2+bs+c=0as^2 + bs + c = 0. For our equation, a=6a = 6, b=−9b = -9, and bb00.
  2. Substitute into quadratic 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}. Substitute a=6a = 6, b=−9b = -9, and c=3c = 3 into the formula. s=−(−9)±(−9)2−4⋅6⋅32⋅6s = \frac{-(-9) \pm \sqrt{(-9)^2 - 4\cdot6\cdot3}}{2\cdot6}
  3. Calculate discriminant: Simplify the equation by calculating the discriminant b2−4ac\sqrt{b^2 - 4ac}.\newlineCalculate the discriminant (−9)2−4⋅6⋅3\sqrt{(-9)^2 - 4\cdot 6\cdot 3}.\newline81−72\sqrt{81 - 72}\newline9\sqrt{9}\newlineThe discriminant is 33.
  4. Insert discriminant value: Continue simplifying the equation by inserting the discriminant value. \newlines=9±312s = \frac{9 \pm 3}{12}\newlineNow, calculate the two possible solutions for ss.\newlines=9+312s = \frac{9 + 3}{12} or s=9−312s = \frac{9 - 3}{12}
  5. Solve for s: Solve for the two possible values of s.\newlines=1212s = \frac{12}{12} or s=612s = \frac{6}{12}\newlines=1s = 1 or s=12s = \frac{1}{2}
  6. Convert fraction to decimal: If necessary, convert the fraction to a decimal rounded to the nearest hundredth.\newlineThe fraction 12\frac{1}{2} is equivalent to 0.500.50 when rounded to the nearest hundredth.

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