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Solve using the quadratic formula.\newline3k2−8k−4=03k^2 - 8k - 4 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinek=k = _____ or k=k = _____

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Q. Solve using the quadratic formula.\newline3k2−8k−4=03k^2 - 8k - 4 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinek=k = _____ or k=k = _____
  1. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation 3k2−8k−4=03k^2 − 8k − 4 = 0. Comparing 3k2−8k−4=03k^2 − 8k − 4 = 0 with the standard form ax2+bx+c=0ax^2 + bx + c = 0, we find: a=3a = 3 b=−8b = -8 c=−4c = -4
  2. Substitute values into formula: Substitute the values of aa, bb, and cc into the quadratic formula, k=−b±b2−4ac2ak = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\newlineThe quadratic formula is k=−(−8)±(−8)2−4⋅3⋅(−4)2⋅3k = \frac{-(-8) \pm \sqrt{(-8)^2 - 4\cdot3\cdot(-4)}}{2\cdot3}.
  3. Simplify expression: Simplify the expression inside the square root and the constants outside the square root.\newlinek=8±64+486k = \frac{8 \pm \sqrt{64 + 48}}{6}\newlinek=8±1126k = \frac{8 \pm \sqrt{112}}{6}
  4. Simplify square root: Simplify the square root 112\sqrt{112} to its simplest radical form.\newline112\sqrt{112} can be simplified to 16×7\sqrt{16\times7}, which is 474\sqrt{7}.\newlinek=8±476k = \frac{8 \pm 4\sqrt{7}}{6}
  5. Divide terms by denominator: Simplify the expression by dividing the terms in the numerator by the denominator.\newlinek=86±476k = \frac{8}{6} \pm \frac{4\sqrt{7}}{6}\newlinek=43±273k = \frac{4}{3} \pm \frac{2\sqrt{7}}{3}
  6. Round if necessary: If necessary, round the decimal values to the nearest hundredth. However, since the question asks for integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth, we can leave the answer in the form of fractions. k=43+273k = \frac{4}{3} + \frac{2\sqrt{7}}{3} or k=43−273k = \frac{4}{3} - \frac{2\sqrt{7}}{3}

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