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Solve using the quadratic formula.\newline2g2+9g+6=02g^2 + 9g + 6 = 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+9g+6=02g^2 + 9g + 6 = 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 ax2+bx+c=0ax^2 + bx + c = 0. In this case, a=2a = 2, b=9b = 9, and c=6c = 6.
  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 92−4(2)(6)9^2 - 4(2)(6).
  3. Discriminant Result: Perform the calculation: 81−48=3381 - 48 = 33.\newlineThe discriminant is 3333, which is a positive number, so there will be two real solutions.
  4. Apply Quadratic Formula: Now, apply the quadratic formula with the calculated discriminant. g=−9±332×2g = \frac{-9 \pm \sqrt{33}}{2 \times 2}
  5. Simplify Equation: Simplify the equation by dividing −9-9 and 33\sqrt{33} by the denominator 44.\newlineg = (−9/4)±(33/4)(-9/4) \pm (\sqrt{33}/4)
  6. Calculate Solutions: The two solutions are then:\newlineg = (−94)+(334)(-\frac{9}{4}) + (\sqrt{\frac{33}{4}}) and g = (−94)−(334)(-\frac{9}{4}) - (\sqrt{\frac{33}{4}})
  7. Express Solutions as Decimals: To express the solutions as decimals rounded to the nearest hundredth, we calculate each one.\newlineFirst solution: g≈(−9/4)+(33/4)≈−2.25+1.44≈−0.81g \approx (-9/4) + (\sqrt{33}/4) \approx -2.25 + 1.44 \approx -0.81\newlineSecond solution: g≈(−9/4)−(33/4)≈−2.25−1.44≈−3.69g \approx (-9/4) - (\sqrt{33}/4) \approx -2.25 - 1.44 \approx -3.69

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