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Solve using the quadratic formula.\newline3w2+5w5=03w^2 + 5w - 5 = 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.\newline3w2+5w5=03w^2 + 5w - 5 = 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 3w2+5w5=03w^2 + 5w - 5 = 0. Comparing 3w2+5w5=03w^2 + 5w - 5 = 0 with the standard form ax2+bx+c=0ax^2 + bx + c = 0, we find: a=3a = 3 b=5b = 5 c=5c = -5
  2. Write quadratic formula: Write down the quadratic formula, which is w=b±b24ac2aw = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula.w=(5)±(5)24(3)(5)2(3)w = \frac{{-\left(5\right) \pm \sqrt{{\left(5\right)^2 - 4\left(3\right)\left(-5\right)}}}}{{2\left(3\right)}}
  4. Simplify discriminant: Simplify the expression under the square root (the discriminant). (5)24(3)(5)=25+60=85\sqrt{(5)^2 - 4(3)(-5)} = \sqrt{25 + 60} = \sqrt{85}
  5. Continue simplifying: Continue simplifying the quadratic formula with the calculated discriminant. w=5±856w = \frac{-5 \pm \sqrt{85}}{6}
  6. Calculate solutions: Calculate the two possible solutions for ww.\newlineFirst solution: w=5+856w = \frac{-5 + \sqrt{85}}{6}\newlineSecond solution: w=5856w = \frac{-5 - \sqrt{85}}{6}
  7. Round values: Round the values of ww to the nearest hundredth, if necessary.\newlineFirst solution: w(5+9.22)/64.22/60.70w \approx (-5 + 9.22) / 6 \approx 4.22 / 6 \approx 0.70\newlineSecond solution: w(59.22)/614.22/62.37w \approx (-5 - 9.22) / 6 \approx -14.22 / 6 \approx -2.37

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