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Solve using the quadratic formula.\newline9g2+g−5=09g^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.\newline9g2+g−5=09g^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. Quadratic Formula: The quadratic formula is given by g=−b±b2−4ac2ag = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients from the quadratic equation in the form ax2+bx+c=0ax^2 + bx + c = 0. For the equation 9g2+g−5=09g^2 + g - 5 = 0, a=9a = 9, b=1b = 1, and c=−5c = -5.
  2. Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac. Here, it is 12−4(9)(−5)1^2 - 4(9)(-5).
  3. Discriminant Calculation: Perform the calculation: 1−4(9)(−5)=1+180=1811 - 4(9)(-5) = 1 + 180 = 181.
  4. Use Quadratic Formula: Now, insert the values of aa, bb, and the discriminant into the quadratic formula to find the two possible values for gg.g=−1±1812⋅9g = \frac{-1 \pm \sqrt{181}}{2 \cdot 9}
  5. Simplify Formula: Simplify the formula by dividing −1-1 and 181\sqrt{181} by 1818.g=(−118)±(18118)g = \left(\frac{-1}{18}\right) \pm \left(\frac{\sqrt{181}}{18}\right)
  6. Calculate Decimal Values: Since 181\sqrt{181} cannot be simplified to an integer or a simple fraction, and the problem asks for decimals if necessary, we will calculate the decimal values of gg rounded to the nearest hundredth.
  7. Calculate Solutions: Calculate the two possible solutions for gg using a calculator:\newlineg=−1+18118≈−1+13.4518≈12.4518≈0.69g = \frac{-1 + \sqrt{181}}{18} \approx \frac{-1 + 13.45}{18} \approx \frac{12.45}{18} \approx 0.69\newlineg=−1−18118≈−1−13.4518≈−14.4518≈−0.80g = \frac{-1 - \sqrt{181}}{18} \approx \frac{-1 - 13.45}{18} \approx \frac{-14.45}{18} \approx -0.80

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