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Solve using the quadratic formula.\newline3w2−w−6=03w^2 - w - 6 = 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−w−6=03w^2 - w - 6 = 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. Identify coefficients: Identify the coefficients of the quadratic equation 3w2−w−6=03w^2 - w - 6 = 0. The standard form of a quadratic equation is ax2+bx+c=0ax^2 + bx + c = 0. By comparing, we find that a=3a = 3, b=−1b = -1, and c=−6c = -6.
  2. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula, w=−b±b2−4ac2aw = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Here, a=3a = 3, b=−1b = -1, and c=−6c = -6. w=−(−1)±(−1)2−4⋅3⋅(−6)2⋅3w = \frac{-(-1) \pm \sqrt{(-1)^2 - 4\cdot3\cdot(-6)}}{2\cdot3}
  3. Calculate discriminant: Simplify the equation by calculating the discriminant (the part under the square root).Discriminant=b2−4ac=(−1)2−4⋅3⋅(−6)=1+72=73\text{Discriminant} = b^2 - 4ac = (-1)^2 - 4\cdot3\cdot(-6) = 1 + 72 = 73
  4. Insert discriminant: Insert the discriminant back into the quadratic formula and simplify.\newlinew=1±736w = \frac{1 \pm \sqrt{73}}{6}
  5. Calculate solutions: Calculate the two possible solutions for ww.w=1+736w = \frac{1 + \sqrt{73}}{6} or w=1−736w = \frac{1 - \sqrt{73}}{6}
  6. Round values: Round the values of ww to the nearest hundredth, if necessary.\newlinew≈(1+8.54)/6w \approx (1 + 8.54) / 6 or w≈(1−8.54)/6w \approx (1 - 8.54) / 6\newlinew≈9.54/6w \approx 9.54 / 6 or w≈−7.54/6w \approx -7.54 / 6\newlinew≈1.59w \approx 1.59 or w≈−1.26w \approx -1.26

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