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Solve using the quadratic formula.\newline3u2−3u−3=03u^2 - 3u - 3 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineu=u = _____ or u=u = _____

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Q. Solve using the quadratic formula.\newline3u2−3u−3=03u^2 - 3u - 3 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineu=u = _____ or u=u = _____
  1. Identify values: Identify the values of aa, bb, and cc in the quadratic equation 3u2−3u−3=03u^2 - 3u - 3 = 0. The quadratic equation is in the form au2+bu+c=0au^2 + bu + c = 0. For our equation, a=3a = 3, b=−3b = -3, and c=−3c = -3.
  2. Substitute in quadratic formula: Substitute the values of aa, bb, and cc into the quadratic formula to find uu. The quadratic formula is u=−b±b2−4ac2au = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substituting the values we get: u=−(−3)±(−3)2−4⋅3⋅(−3)2⋅3u = \frac{-(-3) \pm \sqrt{(-3)^2 - 4\cdot3\cdot(-3)}}{2\cdot3}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant). (−3)2−4⋅3⋅(−3)=9+36=45\sqrt{(-3)^2 - 4\cdot 3\cdot (-3)} = \sqrt{9 + 36} = \sqrt{45}
  4. Continue simplifying formula: Continue simplifying the quadratic formula with the discriminant.\newlineu=3±456u = \frac{3 \pm \sqrt{45}}{6}\newlineSince 45\sqrt{45} can be simplified to 353\sqrt{5}, we can rewrite the expression as:\newlineu=3±356u = \frac{3 \pm 3\sqrt{5}}{6}
  5. Divide numerator by 33: Simplify the expression further by dividing both terms in the numerator by 33.\newlineu=1±52u = \frac{1 \pm \sqrt{5}}{2}
  6. Identify possible values: Identify the two possible values for uu.u=1+52u = \frac{1 + \sqrt{5}}{2} or u=1−52u = \frac{1 - \sqrt{5}}{2}
  7. Round if necessary: If necessary, round the values of uu to the nearest hundredth.\newlineu=1+52≈1+2.242≈3.242≈1.62u = \frac{1 + \sqrt{5}}{2} \approx \frac{1 + 2.24}{2} \approx \frac{3.24}{2} \approx 1.62\newlineu=1−52≈1−2.242≈−1.242≈−0.62u = \frac{1 - \sqrt{5}}{2} \approx \frac{1 - 2.24}{2} \approx \frac{-1.24}{2} \approx -0.62

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