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Solve using the quadratic formula.\newline6w2+7w+2=06w^2 + 7w + 2 = 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.\newline6w2+7w+2=06w^2 + 7w + 2 = 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 values: Identify the values of aa, bb, and cc in the quadratic equation 6w2+7w+2=06w^2 + 7w + 2 = 0. By comparing the equation to the standard form ax2+bx+c=0ax^2 + bx + c = 0, we find: a=6a = 6 b=7b = 7 c=2c = 2
  2. Substitute into formula: Substitute the values of aa, bb, and cc into the quadratic formula w=−b±b2−4ac2aw = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substitute a=6a = 6, b=7b = 7, and c=2c = 2 into the formula. w=−(7)±(7)2−4⋅6⋅22⋅6w = \frac{-(7) \pm \sqrt{(7)^2 - 4\cdot6\cdot2}}{2\cdot6}
  3. Simplify and calculate discriminant: Simplify the expression under the square root and calculate the discriminant b2−4ac\sqrt{b^2 - 4ac}.(7)2−4⋅6⋅2\sqrt{(7)^2 - 4\cdot 6\cdot 2}=49−48= \sqrt{49 - 48}=1= \sqrt{1}
  4. Calculate solutions: Calculate the two possible solutions for ww.\newlineSince the discriminant is 11, we have:\newlinew=−7±12×6w = \frac{-7 \pm 1}{2 \times 6}\newlineThis gives us two solutions:\newlinew=−7+112w = \frac{-7 + 1}{12} and w=−7−112w = \frac{-7 - 1}{12}
  5. Simplify solutions: Simplify both solutions.\newlineFor the first solution:\newlinew=−7+112w = \frac{-7 + 1}{12}\newlinew=−612w = \frac{-6}{12}\newlinew=−12w = -\frac{1}{2}\newlineFor the second solution:\newlinew=−7−112w = \frac{-7 - 1}{12}\newlinew=−812w = \frac{-8}{12}\newlinew=−23w = -\frac{2}{3}\newlineBoth fractions are already in simplest form.
  6. Simplify solutions: Simplify both solutions.\newlineFor the first solution:\newlinew=−7+112w = \frac{-7 + 1}{12}\newlinew=−612w = \frac{-6}{12}\newlinew=−12w = -\frac{1}{2}\newlineFor the second solution:\newlinew=−7−112w = \frac{-7 - 1}{12}\newlinew=−812w = \frac{-8}{12}\newlinew=−23w = -\frac{2}{3}\newlineBoth fractions are already in simplest form.If necessary, round the solutions to the nearest hundredth.\newlineHowever, since both solutions are fractions in simplest form, there is no need to round to the nearest hundredth.

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