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Solve using the quadratic formula.\newline8w2−9w−9=08w^2 - 9w - 9 = 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−9=08w^2 - 9w - 9 = 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−9=08w^2 − 9w − 9 = 0. Comparing the equation with the standard form ax2+bx+c=0ax^2 + bx + c = 0, we find: a=8a = 8 b=−9b = -9 c=−9c = -9
  2. Write quadratic formula: Write down the quadratic formula, which is 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.\newlinew=−(−9)±(−9)2−4⋅8⋅(−9)2⋅8w = \frac{-(-9) \pm \sqrt{(-9)^2 - 4 \cdot 8 \cdot (-9)}}{2 \cdot 8}\newlinew=9±81+28816w = \frac{9 \pm \sqrt{81 + 288}}{16}
  4. Simplify expression: Simplify the expression under the square root and the entire equation. w=9±36916w = \frac{9 \pm \sqrt{369}}{16}
  5. Calculate square root: Calculate the square root of 369369 to find the two possible solutions for ww.369≈19.21\sqrt{369} \approx 19.21w=(9+19.21)16w = \frac{(9 + 19.21)}{16} or w=(9−19.21)16w = \frac{(9 - 19.21)}{16}
  6. Simplify solutions: Simplify the two solutions for ww.
    w≈(9+19.21)/16w \approx (9 + 19.21) / 16 or w≈(9−19.21)/16w \approx (9 - 19.21) / 16
    w≈28.21/16w \approx 28.21 / 16 or w≈−10.21/16w \approx -10.21 / 16
    w≈1.76w \approx 1.76 or w≈−0.64w \approx -0.64
  7. Round to nearest hundredth: Round the solutions to the nearest hundredth as required. w≈1.76w \approx 1.76 or w≈−0.64w \approx -0.64

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