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Solve using the quadratic formula.\newline2v2−7v+2=02v^2 - 7v + 2 = 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.\newline2v2−7v+2=02v^2 - 7v + 2 = 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, and cc: Identify values of aa, bb, and cc from the equation 2v2−7v+2=02v^2 − 7v + 2 = 0.a=2a = 2, b=−7b = -7, c=2c = 2.
  2. Plug values into quadratic formula: Plug aa, bb, and cc into the quadratic formula: v=−b±b2−4ac2a.v = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Calculate the discriminant: Calculate the discriminant: b2−4ac=(−7)2−4⋅2⋅2.\sqrt{b^2 - 4ac} = \sqrt{(-7)^2 - 4\cdot 2\cdot 2}.
  4. Simplify the discriminant: Simplify the discriminant: 49−16=33.\sqrt{49 - 16} = \sqrt{33}.
  5. Write out full quadratic formula: Write out the full quadratic formula with values: v=−(−7)±332×2v = \frac{-(-7) \pm \sqrt{33}}{2 \times 2}.
  6. Simplify the formula: Simplify the formula: v=7±334v = \frac{7 \pm \sqrt{33}}{4}.
  7. Calculate possible solutions for v: Calculate the two possible solutions for v: v=7+334v = \frac{7 + \sqrt{33}}{4} or v=7−334v = \frac{7 - \sqrt{33}}{4}.
  8. Round values to nearest hundredth: Round the values of vv to the nearest hundredth, if necessary: v≈(7+5.74)/4v \approx (7 + 5.74) / 4 or v≈(7−5.74)/4v \approx (7 - 5.74) / 4.
  9. Simplify the fractions: Simplify the fractions: v≈12.744v \approx \frac{12.74}{4} or v≈1.264.v \approx \frac{1.26}{4}.

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