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Solve using the quadratic formula.\newline6s2−2s−8=06s^2 - 2s - 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.\newline6s2−2s−8=06s^2 - 2s - 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 6s2−2s−8=06s^2 − 2s − 8 = 0. The quadratic equation is in the form as2+bs+c=0as^2 + bs + c = 0. Comparing this with our equation, we get: a=6a = 6 b=−2b = -2 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=−2b = -2, and c=−8c = -8 into the formula. s=−(−2)±(−2)2−4⋅6⋅(−8)2⋅6s = \frac{-(-2) \pm \sqrt{(-2)^2 - 4\cdot6\cdot(-8)}}{2\cdot6}
  3. Simplify expression and constants: Simplify the expression under the square root and the constants outside the square root.\newlineCalculate (−2)2(-2)^2, 4×6×(−8)4\times6\times(-8), and 2×62\times6.\newline(−2)2=4(-2)^2 = 4\newline4×6×(−8)=−1924\times6\times(-8) = -192\newline2×6=122\times6 = 12\newlineNow substitute these values back into the formula.\newlines=2±4+19212s = \frac{2 \pm \sqrt{4 + 192}}{12}
  4. Simplify expression inside square root: Simplify the expression inside the square root and then the square root itself.\newlineCalculate 4+1924 + 192.\newline4+192=1964 + 192 = 196\newlineNow take the square root of 196196.\newline196=14\sqrt{196} = 14\newlineNow substitute this value back into the formula.\newlines=(2±14)/12s = (2 \pm 14) / 12
  5. Calculate two possible solutions: Calculate the two possible solutions for ss.\newlineFirst solution:\newlines=(2+14)/12s = (2 + 14) / 12\newlines=16/12s = 16 / 12\newlines=4/3s = 4 / 3\newlineSecond solution:\newlines=(2−14)/12s = (2 - 14) / 12\newlines=−12/12s = -12 / 12\newlines=−1s = -1
  6. Write final answers: Simplify the fractions and write the final answers.\newlineThe first solution 43\frac{4}{3} is already in its simplest form.\newlineThe second solution −1-1 is an integer.\newlineSo the final answers are:\newlines=43s = \frac{4}{3} or s=−1s = -1

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