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Solve using the quadratic formula.\newline9v2−v−4=09v^2 - v - 4 = 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.\newline9v2−v−4=09v^2 - v - 4 = 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. Quadratic Formula Explanation: The quadratic formula is given by v=−b±b2−4ac2av = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients of the terms in the quadratic equation av2+bv+c=0av^2 + bv + c = 0. In this case, a=9a = 9, b=−1b = -1, and c=−4c = -4.
  2. Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac. Here, it is (−1)2−4(9)(−4)(-1)^2 - 4(9)(-4).
  3. Discriminant Calculation: Perform the calculation: 1−4(9)(−4)=1+144=1451 - 4(9)(-4) = 1 + 144 = 145.
  4. Insert Values into Formula: Now, insert the values of aa, bb, and the discriminant into the quadratic formula to find the two possible values for vv.v=−(−1)±1452×9v = \frac{-(-1) \pm \sqrt{145}}{2 \times 9}v=1±14518v = \frac{1 \pm \sqrt{145}}{18}
  5. Simplify Solutions: Simplify the two possible solutions for vv:v=1+14518v = \frac{1 + \sqrt{145}}{18} or v=1−14518v = \frac{1 - \sqrt{145}}{18}
  6. Calculate Decimal Values: Since 145\sqrt{145} cannot be simplified to an integer or a simple fraction, and the problem asks for the answer to be in simplest form or as a decimal rounded to the nearest hundredth, we will calculate the decimal values.\newlinev≈(1+12.04)/18v \approx (1 + 12.04) / 18 or v≈(1−12.04)/18v \approx (1 - 12.04) / 18\newlinev≈13.04/18v \approx 13.04 / 18 or v≈−11.04/18v \approx -11.04 / 18
  7. Perform Division: Now, perform the division to get the decimal values: v≈0.724v \approx 0.724 or v≈−0.613v \approx -0.613 (rounded to the nearest hundredth).

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