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Solve using the quadratic formula.\newline8w2−9w−4=08w^2 - 9w - 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.\newline8w2−9w−4=08w^2 - 9w - 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. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation 8w2−9w−4=08w^2 − 9w − 4 = 0.a=8a = 8, b=−9b = -9, c=−4c = -4
  2. Write quadratic formula: Write down the quadratic formula: w=−b±b2−4ac2aw = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula.w=−(−9)±(−9)2−4⋅8⋅(−4)2⋅8w = \frac{-(-9) \pm \sqrt{(-9)^2 - 4 \cdot 8 \cdot (-4)}}{2 \cdot 8}
  4. Simplify equation: Simplify the equation by calculating the discriminant b2−4acb^2 - 4ac.\newlineDiscriminant = (−9)2−4⋅8⋅(−4)(-9)^2 - 4\cdot8\cdot(-4) = 81+12881 + 128 = 209209
  5. Insert discriminant: Insert the discriminant back into the quadratic formula. w=9±20916w = \frac{9 \pm \sqrt{209}}{16}
  6. Calculate solutions: Calculate the two possible solutions for ww.w=9+20916w = \frac{9 + \sqrt{209}}{16} or w=9−20916w = \frac{9 - \sqrt{209}}{16}
  7. Round values: Round the values of ww to the nearest hundredth, if necessary.w≈(9+14.456)/16w \approx (9 + 14.456) / 16 or w≈(9−14.456)/16w \approx (9 - 14.456) / 16w≈23.456/16w \approx 23.456 / 16 or w≈−5.456/16w \approx -5.456 / 16w≈1.47w \approx 1.47 or w≈−0.34w \approx -0.34

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