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Solve using the quadratic formula.\newline2g2−g−5=02g^2 - g - 5 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineg=g = _____ or g=g = _____

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Q. Solve using the quadratic formula.\newline2g2−g−5=02g^2 - g - 5 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineg=g = _____ or g=g = _____
  1. Identify coefficients: Identify coefficients aa, bb, and cc from the quadratic equation 2g2−g−5=02g^2 - g - 5 = 0, where a=2a=2, b=−1b=-1, and c=−5c=-5.
  2. Write down formula: Write down the quadratic formula: g=−b±b2−4ac2ag = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Plug coefficients: Plug the coefficients into the quadratic formula: g=1±(−1)2−4(2)(−5)2(2)g = \frac{1 \pm \sqrt{(-1)^2 - 4(2)(-5)}}{2(2)}.
  4. Simplify square root: Simplify inside the square root: g=1±1+404g = \frac{1 \pm \sqrt{1 + 40}}{4}.
  5. Further simplify: Further simplify the square root: g=1±414g = \frac{1 \pm \sqrt{41}}{4}.
  6. Split into equations: Split into two equations for the plus and minus: g=1+414g = \frac{1 + \sqrt{41}}{4} or g=1−414g = \frac{1 - \sqrt{41}}{4}.
  7. Calculate values: Calculate the values: g≈(1+6.40)/4g \approx (1 + 6.40) / 4 or g≈(1−6.40)/4g \approx (1 - 6.40) / 4.

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