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Solve using the quadratic formula.\newlineg2+7g+9=0g^2 + 7g + 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.\newlineg2+7g+9=0g^2 + 7g + 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. 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 of the terms in the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0. In this case, a=1a = 1, b=7b = 7, and c=9c = 9.
  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 72−4(1)(9)=49−36=137^2 - 4(1)(9) = 49 - 36 = 13.
  3. Apply Quadratic Formula: Now, apply the quadratic formula with the values of aa, bb, and cc:g=−7±132×1g = \frac{{-7 \pm \sqrt{13}}}{{2 \times 1}}g=−7±132g = \frac{{-7 \pm \sqrt{13}}}{2}
  4. Solutions as Irrational Numbers: Since the discriminant is positive but not a perfect square, the solutions will be irrational numbers. We cannot simplify 13\sqrt{13} to a rational number, so we leave it as is and write the solutions as:\newlineg=−7+132g = \frac{-7 + \sqrt{13}}{2} or g=−7−132g = \frac{-7 - \sqrt{13}}{2}
  5. Solutions as Decimals: To express the solutions as decimals rounded to the nearest hundredth, we calculate each one:\newlineg=−7+132≈−7+3.612≈−3.392≈−1.70g = \frac{-7 + \sqrt{13}}{2} \approx \frac{-7 + 3.61}{2} \approx \frac{-3.39}{2} \approx -1.70\newlineg=−7−132≈−7−3.612≈−10.612≈−5.30g = \frac{-7 - \sqrt{13}}{2} \approx \frac{-7 - 3.61}{2} \approx \frac{-10.61}{2} \approx -5.30

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