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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 coefficients: Identify the coefficients of the quadratic equation.\newlineThe quadratic equation is in the form ax2+bx+c=0ax^2 + bx + c = 0. For the equation 6w2+7w−2=06w^2 + 7w - 2 = 0, the coefficients are:\newlinea = 66\newlineb = 77\newlinec = −2-2
  2. Substitute into formula: Substitute the coefficients into the quadratic formula.\newlineThe quadratic formula is w=−b±b2−4ac2aw = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substituting the values we get:\newlinew=−(7)±(7)2−4(6)(−2)2(6)w = \frac{-(7) \pm \sqrt{(7)^2 - 4(6)(-2)}}{2(6)}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant).\newlineCalculate the discriminant: (7)2−4(6)(−2)=49+48=97(7)^2 - 4(6)(-2) = 49 + 48 = 97
  4. Continue with formula: Continue with the quadratic formula using the discriminant.\newlinew=−7±972(6)w = \frac{-7 \pm \sqrt{97}}{2(6)}\newlinew=−7±9712w = \frac{-7 \pm \sqrt{97}}{12}
  5. Calculate solutions: Calculate the two possible solutions for ww.\newlineFirst solution: w=−7+9712w = \frac{-7 + \sqrt{97}}{12}\newlineSecond solution: w=−7−9712w = \frac{-7 - \sqrt{97}}{12}
  6. Simplify and round: Simplify the solutions and, if necessary, round to the nearest hundredth.\newlineFirst solution: w≈(−7+9.8512)≈2.8512≈0.24w \approx (\frac{-7 + 9.85}{12}) \approx \frac{2.85}{12} \approx 0.24\newlineSecond solution: w≈(−7−9.8512)≈−16.8512≈−1.40w \approx (\frac{-7 - 9.85}{12}) \approx \frac{-16.85}{12} \approx -1.40

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