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Solve using the quadratic formula.\newline9f2−6f−3=09f^2 - 6f - 3 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinef=f = _____ or f=f = _____

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Q. Solve using the quadratic formula.\newline9f2−6f−3=09f^2 - 6f - 3 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinef=f = _____ or f=f = _____
  1. Identify values quadratic equation: Identify the values of aa, bb, and cc in the quadratic equation 9f2−6f−3=09f^2 - 6f - 3 = 0. By comparing the equation to the standard form ax2+bx+c=0ax^2 + bx + c = 0, we find: a=9a = 9 b=−6b = -6 c=−3c = -3
  2. Substitute values quadratic formula: Substitute the values of aa, bb, and cc into the quadratic formula f=−b±b2−4ac2af = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Here, we have: f=−(−6)±(−6)2−4⋅9⋅(−3)2⋅9f = \frac{-(-6) \pm \sqrt{(-6)^2 - 4 \cdot 9 \cdot (-3)}}{2 \cdot 9}
  3. Simplify expression square root: Simplify the expression under the square root (the discriminant). (−6)2−4⋅9⋅(−3)=36+108=144\sqrt{(-6)^2 - 4\cdot 9\cdot (-3)} = \sqrt{36 + 108} = \sqrt{144}
  4. Continue simplifying quadratic formula: Continue simplifying the quadratic formula with the calculated discriminant.\newlinef=6±14418f = \frac{6 \pm \sqrt{144}}{18}\newlineSince 144=12\sqrt{144} = 12, we have:\newlinef=6±1218f = \frac{6 \pm 12}{18}
  5. Find possible values: Find the two possible values for ff.f=6+1218f = \frac{6 + 12}{18} or f=6−1218f = \frac{6 - 12}{18}f=1818f = \frac{18}{18} or f=−618f = \frac{-6}{18}f=1f = 1 or f=−13f = -\frac{1}{3}

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