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Solve using the quadratic formula.\newline3r2−8r−6=03r^2 - 8r - 6 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliner=r = _____ or r=r = _____

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Q. Solve using the quadratic formula.\newline3r2−8r−6=03r^2 - 8r - 6 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliner=r = _____ or r=r = _____
  1. Identify values of aa, bb, cc: Identify the values of aa, bb, and cc in the quadratic equation 3r2−8r−6=03r^2 − 8r − 6 = 0. By comparing the equation to the standard form ax2+bx+c=0ax^2 + bx + c = 0, we find: a=3a = 3 b=−8b = -8 bb00
  2. Substitute into quadratic formula: Substitute the values of aa, bb, and cc into the quadratic formula r=−b±b2−4ac2ar = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Here, we have: r=−(−8)±(−8)2−4⋅3⋅(−6)2⋅3r = \frac{-(-8) \pm \sqrt{(-8)^2 - 4 \cdot 3 \cdot (-6)}}{2 \cdot 3}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant). (−8)2−4⋅3⋅(−6)=64+72=136\sqrt{(-8)^2 - 4 \cdot 3 \cdot (-6)} = \sqrt{64 + 72} = \sqrt{136}
  4. Continue simplifying formula: Continue simplifying the quadratic formula with the values we have.\newliner=8±1366r = \frac{8 \pm \sqrt{136}}{6}
  5. Simplify square root: Simplify the square root of 136136 to its decimal form to prepare for the final calculation.\newline136≈11.66\sqrt{136} \approx 11.66 (rounded to the nearest hundredth)
  6. Calculate possible values for r: Calculate the two possible values for r using the simplified square root. \newliner=8+11.666r = \frac{8 + 11.66}{6} or r=8−11.666r = \frac{8 - 11.66}{6}\newliner≈19.666r \approx \frac{19.66}{6} or r≈−3.666r \approx \frac{-3.66}{6}\newliner≈3.28r \approx 3.28 or r≈−0.61r \approx -0.61 (rounded to the nearest hundredth)

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