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Solve using the quadratic formula.\newline9g2−4g−1=09g^2 - 4g - 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.\newline9g2−4g−1=09g^2 - 4g - 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 9g2−4g−1=09g^2 − 4g − 1 = 0. Comparing the equation with the standard form ax2+bx+c=0ax^2 + bx + c = 0, we find: a=9a = 9 b=−4b = -4 c=−1c = -1
  2. Substitute in formula: Substitute the values of aa, bb, and cc into the quadratic formula g=−b±b2−4ac2ag = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\newlineg=−(−4)±(−4)2−4⋅9⋅(−1)2⋅9g = \frac{-(-4) \pm \sqrt{(-4)^2 - 4\cdot9\cdot(-1)}}{2\cdot9}
  3. Simplify expression: Simplify the expression under the square root and the constants outside the square root. \newlineg=4±16+3618g = \frac{4 \pm \sqrt{16 + 36}}{18}\newlineg=4±5218g = \frac{4 \pm \sqrt{52}}{18}
  4. Simplify square root: Simplify the square root. 52\sqrt{52} can be simplified to 2132\sqrt{13} because 52=4×1352 = 4 \times 13. g=4±21318g = \frac{4 \pm 2\sqrt{13}}{18}
  5. Divide by 22: Simplify the expression by dividing all terms by 22.g=2±139g = \frac{2 \pm \sqrt{13}}{9}
  6. Identify possible values: Identify the two possible values for gg.g=2+139g = \frac{2 + \sqrt{13}}{9} or g=2−139g = \frac{2 - \sqrt{13}}{9}
  7. Round to nearest hundredth: Round the values of gg to the nearest hundredth, if necessary.g≈(2+3.61)9g \approx \frac{(2 + 3.61)}{9} or g≈(2−3.61)9g \approx \frac{(2 - 3.61)}{9}g≈5.619g \approx \frac{5.61}{9} or g≈−1.619g \approx \frac{-1.61}{9}g≈0.62g \approx 0.62 or g≈−0.18g \approx -0.18

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