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Solve using the quadratic formula.\newline4v2−9v+3=04v^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.\newline4v2−9v+3=04v^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. Identify values of aa, bb, cc: Identify the values of aa, bb, and cc from the quadratic equation 4v2−9v+3=04v^2 − 9v + 3 = 0.\newlineBy comparing 4v2−9v+3=04v^2 − 9v + 3 = 0 with the standard form ax2+bx+c=0ax^2 + bx + c = 0, we find:\newlinea=4a = 4\newlinebb00\newlinebb11
  2. Substitute into quadratic formula: Substitute the values of aa, bb, and cc into the quadratic formula v=−b±b2−4ac2av = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substitute a=4a = 4, b=−9b = -9, and c=3c = 3 into the quadratic formula. v=−(−9)±(−9)2−4⋅4⋅32⋅4v = \frac{-(-9) \pm \sqrt{(-9)^2 - 4\cdot4\cdot3}}{2\cdot4} v=9±81−488v = \frac{9 \pm \sqrt{81 - 48}}{8}
  3. Simplify and calculate discriminant: Simplify the expression under the square root and calculate the discriminant. \newline81−48\sqrt{81 - 48}\newline= 33\sqrt{33}\newlineNow we have:\newlinev=9±338v = \frac{9 \pm \sqrt{33}}{8}
  4. Calculate possible solutions for vv: Calculate the two possible solutions for vv.v=9+338v = \frac{9 + \sqrt{33}}{8} or v=9−338v = \frac{9 - \sqrt{33}}{8}
  5. Round values of vv: If necessary, round the values of vv to the nearest hundredth.v≈(9+5.74)/8v \approx (9 + 5.74) / 8 or v≈(9−5.74)/8v \approx (9 - 5.74) / 8v≈14.74/8v \approx 14.74 / 8 or v≈3.26/8v \approx 3.26 / 8v≈1.84v \approx 1.84 or v≈0.41v \approx 0.41

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