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Solve using the quadratic formula.\newline6v2+9v−8=06v^2 + 9v - 8 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinev=v = _____ or v=v = _____

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Q. Solve using the quadratic formula.\newline6v2+9v−8=06v^2 + 9v - 8 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinev=v = _____ or v=v = _____
  1. Plug Values into Formula: Plug the values of aa, bb, and cc into the quadratic formula, v=−b±b2−4ac2av = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. So, v=−(9)±(9)2−4⋅6⋅(−8)2⋅6v = \frac{-(9) \pm \sqrt{(9)^2 - 4\cdot6\cdot(-8)}}{2\cdot6}.
  2. Simplify Square Root: Simplify inside the square root: (9)2−4⋅6⋅(−8)=81+192\sqrt{(9)^2 - 4\cdot6\cdot(-8)} = \sqrt{81 + 192}.\newlineThis gives us 273\sqrt{273}.
  3. Calculate Possible Solutions: Now, calculate the two possible solutions for vv.v=−9±27312v = \frac{{-9 \pm \sqrt{273}}}{{12}}.
  4. Simplify Solutions: Simplify the solutions. v=−9+27312v = \frac{-9 + \sqrt{273}}{12} or v=−9−27312v = \frac{-9 - \sqrt{273}}{12}.
  5. Round to Nearest Hundredth: Round the values of vv to the nearest hundredth if necessary.v≈(−9+16.52)/12v \approx (-9 + 16.52) / 12 or v≈(−9−16.52)/12v \approx (-9 - 16.52) / 12.v≈7.52/12v \approx 7.52 / 12 or v≈−25.52/12v \approx -25.52 / 12.
  6. Divide to Get Decimal Values: Finally, divide to get the decimal values. v≈0.63v \approx 0.63 or v≈−2.13v \approx -2.13.

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