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Solve using the quadratic formula.\newline7g2−8g−9=07g^2 - 8g - 9 = 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.\newline7g2−8g−9=07g^2 - 8g - 9 = 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 of aa, bb, cc: Identify the values of aa, bb, and cc in the quadratic equation 7g2−8g−9=07g^2 − 8g − 9 = 0. Compare 7g2−8g−9=07g^2 − 8g − 9 = 0 with the standard form ax2+bx+c=0ax^2 + bx + c = 0. a=7a = 7 bb00 bb11
  2. Substitute values into quadratic 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}. Substitute a=7a = 7, b=−8b = -8, and c=−9c = -9 into the formula. g=−(−8)±(−8)2−4⋅7⋅(−9)2⋅7g = \frac{-(-8) \pm \sqrt{(-8)^2 - 4\cdot7\cdot(-9)}}{2\cdot7} g=8±64+25214g = \frac{8 \pm \sqrt{64 + 252}}{14}
  3. Simplify expression and calculate discriminant: Simplify the expression under the square root and calculate the discriminant.64+252\sqrt{64 + 252} = 316\sqrt{316}
  4. Continue with quadratic formula: Continue with the quadratic formula using the simplified discriminant.\newlineg=8±31614g = \frac{8 \pm \sqrt{316}}{14}\newlineCalculate the two possible solutions for gg.\newlineg=8+31614g = \frac{8 + \sqrt{316}}{14} or g=8−31614g = \frac{8 - \sqrt{316}}{14}
  5. Simplify solutions and round: Simplify the solutions and, if necessary, round to the nearest hundredth.\newlineg=8+31614g = \frac{8 + \sqrt{316}}{14} or g=8−31614g = \frac{8 - \sqrt{316}}{14}\newlineg≈8+17.7814g \approx \frac{8 + 17.78}{14} or g≈8−17.7814g \approx \frac{8 - 17.78}{14}\newlineg≈25.7814g \approx \frac{25.78}{14} or g≈−9.7814g \approx \frac{-9.78}{14}\newlineg≈1.84g \approx 1.84 or g≈−0.70g \approx -0.70

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