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Solve using the quadratic formula.\newline5g2−7g+1=05g^2 - 7g + 1 = 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.\newline5g2−7g+1=05g^2 - 7g + 1 = 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 values: Identify the values of aa, bb, and cc in the quadratic equation 5g2−7g+1=05g^2 − 7g + 1 = 0. The quadratic equation is in the form ag2+bg+c=0ag^2 + bg + c = 0, so by comparison: a=5a = 5 b=−7b = -7 c=1c = 1
  2. Substitute values into formula: Substitute the values of aa, bb, and cc into the quadratic formula to find gg. The quadratic formula is g=−b±b2−4ac2ag = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substituting the values we get: g=−(−7)±(−7)2−4⋅5⋅12⋅5g = \frac{-(-7) \pm \sqrt{(-7)^2 - 4\cdot5\cdot1}}{2\cdot5}
  3. Simplify terms and constants: Simplify the terms under the square root and the constants outside the square root.\newlineg=7±49−2010g = \frac{7 \pm \sqrt{49 - 20}}{10}\newlineg=7±2910g = \frac{7 \pm \sqrt{29}}{10}
  4. Identify possible values: Identify the two possible values for gg.g=7+2910g = \frac{7 + \sqrt{29}}{10} or g=7−2910g = \frac{7 - \sqrt{29}}{10}
  5. Round values if necessary: If necessary, round the values of gg to the nearest hundredth.\newlineg≈(7+5.39)/10g \approx (7 + 5.39) / 10 or g≈(7−5.39)/10g \approx (7 - 5.39) / 10\newlineg≈12.39/10g \approx 12.39 / 10 or g≈1.61/10g \approx 1.61 / 10\newlineg≈1.24g \approx 1.24 or g≈0.16g \approx 0.16

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