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Solve using the quadratic formula.\newline4g2−4g−3=04g^2 - 4g - 3 = 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.\newline4g2−4g−3=04g^2 - 4g - 3 = 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 4g2−4g−3=04g^2 − 4g − 3 = 0. The quadratic equation is in the form ag2+bg+c=0ag^2 + bg + c = 0, so by comparison: a=4a = 4 b=−4b = -4 bb00
  2. Substitute values into formula: Substitute the values of aa, bb, and cc into the quadratic formula to find gg. The quadratic formula is g=−b±b2−4ac2ag = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substituting the values we get: g=−(−4)±(−4)2−4⋅4⋅(−3)2⋅4g = \frac{-(-4) \pm \sqrt{(-4)^2 - 4\cdot4\cdot(-3)}}{2\cdot4}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant). (−4)2−4⋅4⋅(−3)=16+48=64\sqrt{(-4)^2 - 4\cdot 4\cdot (-3)} = \sqrt{16 + 48} = \sqrt{64}
  4. Continue simplifying formula: Continue simplifying the quadratic formula with the calculated discriminant. g=4±648g = \frac{4 \pm \sqrt{64}}{8}
  5. Solve for possible values: Solve for the two possible values of gg.g=4+88g = \frac{4 + 8}{8} or g=4−88g = \frac{4 - 8}{8}g=128g = \frac{12}{8} or g=−48g = \frac{-4}{8}
  6. Simplify final answers: Simplify the fractions to get the final answers.\newlineg=128g = \frac{12}{8} simplifies to g=32g = \frac{3}{2} or g=1.5g = 1.5\newlineg=−48g = \frac{-4}{8} simplifies to g=−12g = \frac{-1}{2} or g=−0.5g = -0.5

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