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Solve using the quadratic formula.\newline3w2+8w+4=03w^2 + 8w + 4 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinew=w = _____ or w=w = _____

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Q. Solve using the quadratic formula.\newline3w2+8w+4=03w^2 + 8w + 4 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinew=w = _____ or w=w = _____
  1. Quadratic Formula Explanation: The quadratic formula is given by w=−b±b2−4ac2aw = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients of the terms in the quadratic equation aw2+bw+c=0aw^2 + bw + c = 0. In this case, a=3a = 3, b=8b = 8, 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 82−4(3)(4)8^2 - 4(3)(4).
  3. Discriminant Calculation: Perform the calculation: 64−48=1664 - 48 = 16.
  4. Insert Values into Formula: Now, insert the values into the quadratic formula. Since the discriminant is 1616, which is a perfect square, we will get exact values for ww. \newlinew=−8±162×3w = \frac{-8 \pm \sqrt{16}}{2 \times 3}
  5. Simplify Square Root: Simplify the square root: 16=4\sqrt{16} = 4. w=−8±46w = \frac{-8 \pm 4}{6}
  6. Solve for First Value: Now, solve for the two possible values of ww.
    First solution: w=(−8+4)/6=−4/6=−2/3w = (-8 + 4) / 6 = -4 / 6 = -2 / 3
    Second solution: w=(−8−4)/6=−12/6=−2w = (-8 - 4) / 6 = -12 / 6 = -2

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