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Solve using the quadratic formula.\newline9g2+2g−6=09g^2 + 2g - 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.\newline9g2+2g−6=09g^2 + 2g - 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. Identify coefficients: Identify the coefficients of the quadratic equation 9g2+2g−6=09g^2 + 2g - 6 = 0. The standard form of a quadratic equation is ax2+bx+c=0ax^2 + bx + c = 0. Here, a=9a = 9, b=2b = 2, and c=−6c = -6.
  2. Write formula: Write down the quadratic formula.\newlineThe quadratic formula is given by w=−b±b2−4ac2aw = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula.g=−2±22−4⋅9⋅(−6)2⋅9g = \frac{-2 \pm \sqrt{2^2 - 4 \cdot 9 \cdot (-6)}}{2 \cdot 9}
  4. Simplify discriminant: Simplify the expression under the square root (the discriminant). 22−4⋅9⋅(−6)=4+216=220\sqrt{2^2 - 4 \cdot 9 \cdot (-6)} = \sqrt{4 + 216} = \sqrt{220}
  5. Simplify square root: Simplify the square root of 220220.220\sqrt{220} can be simplified to 2552\sqrt{55} because 220=4×55220 = 4\times55.
  6. Substitute back: Substitute the simplified square root back into the formula. g=−2±25518g = \frac{-2 \pm 2\sqrt{55}}{18}
  7. Divide by 22: Simplify the expression by dividing all terms by 22.g=−1±559g = \frac{-1 \pm \sqrt{55}}{9}
  8. Calculate solutions: Calculate the two possible solutions for gg.g=−1+559g = \frac{{-1 + \sqrt{55}}}{{9}} or g=−1−559g = \frac{{-1 - \sqrt{55}}}{{9}}
  9. Round values: Round the values of gg to the nearest hundredth, if required.g≈(−1+7.42)/9g \approx (-1 + 7.42) / 9 or g≈(−1−7.42)/9g \approx (-1 - 7.42) / 9g≈6.42/9g \approx 6.42 / 9 or g≈−8.42/9g \approx -8.42 / 9g≈0.71g \approx 0.71 or g≈−0.93g \approx -0.93

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