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Solve using the quadratic formula.\newline6v2−9v+3=06v^2 - 9v + 3 = 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+3=06v^2 - 9v + 3 = 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 into Quadratic Formula: Plug 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⋅32⋅6v = \frac{-(-9) \pm \sqrt{(-9)^2 - 4\cdot6\cdot3}}{2\cdot6}.
  2. Simplify Square Root: Simplify inside the square root: 81−72\sqrt{81 - 72}.\newlineThis gives us 9\sqrt{9}.
  3. Calculate Values for vv: Now, calculate the values for vv: v=9±912v = \frac{9 \pm \sqrt{9}}{12}.\newlineSo, v=9±312v = \frac{9 \pm 3}{12}.
  4. Find Possible Solutions for vv: Find the two possible solutions for vv: v=9+312v = \frac{9 + 3}{12} or v=9−312v = \frac{9 - 3}{12}. This simplifies to v=1212v = \frac{12}{12} or v=612v = \frac{6}{12}.
  5. Simplify Fractions: Simplify the fractions: v=1v = 1 or v=12v = \frac{1}{2}.\newlineSince 612\frac{6}{12} reduces to 12\frac{1}{2}.
  6. Check for Rounding: Check if the solutions need to be rounded to the nearest hundredth. Since both solutions are already in simplest form and are exact values, no rounding is necessary.

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