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Solve using the quadratic formula.\newline7w2+2w−6=07w^2 + 2w - 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.\newline7w2+2w−6=07w^2 + 2w - 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 values: Identify the values of aa, bb, and cc in the quadratic equation 7w2+2w−6=07w^2 + 2w - 6 = 0. By comparing 7w2+2w−6=07w^2 + 2w - 6 = 0 with the standard form ax2+bx+c=0ax^2 + bx + c = 0, we find: a=7a = 7 b=2b = 2 c=−6c = -6
  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=7a = 7, b=2b = 2, and c=−6c = -6 into the formula. w=−(2)±(2)2−4⋅7⋅(−6)2⋅7w = \frac{-(2) \pm \sqrt{(2)^2 - 4\cdot7\cdot(-6)}}{2\cdot7}
  3. Simplify expression: Simplify the expression under the square root and calculate its value.\newline(2)2−4⋅7⋅(−6)\sqrt{(2)^2 - 4\cdot7\cdot(-6)}\newline= 4+168\sqrt{4 + 168}\newline= 172\sqrt{172}
  4. Simplify quadratic formula: Simplify the quadratic formula with the calculated square root value.\newlinew=−2±1722×7w = \frac{-2 \pm \sqrt{172}}{2\times7}\newlinew=−2±17214w = \frac{-2 \pm \sqrt{172}}{14}
  5. Calculate solutions: Calculate the two possible solutions for ww.\newlineFirst solution:\newlinew=−2+17214w = \frac{{-2 + \sqrt{172}}}{{14}}\newlineSecond solution:\newlinew=−2−17214w = \frac{{-2 - \sqrt{172}}}{{14}}
  6. Round values: Round the values of ww to the nearest hundredth, if necessary.\newlineFirst solution:\newlinew≈(−2+13.11)/14w \approx (-2 + 13.11) / 14\newlinew≈11.11/14w \approx 11.11 / 14\newlinew≈0.79w \approx 0.79\newlineSecond solution:\newlinew≈(−2−13.11)/14w \approx (-2 - 13.11) / 14\newlinew≈−15.11/14w \approx -15.11 / 14\newlinew≈−1.08w \approx -1.08

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