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Solve using the quadratic formula.\newline9f2+4f−6=09f^2 + 4f - 6 = 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+4f−6=09f^2 + 4f - 6 = 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 coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation 9f2+4f−6=09f^2 + 4f - 6 = 0 by comparing it to the standard form ax2+bx+c=0ax^2 + bx + c = 0.\newlinea=9a = 9\newlineb=4b = 4\newlinec=−6c = -6
  2. Substitute values into 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}.f=−(4)±(4)2−4⋅(9)⋅(−6)2⋅(9)f = \frac{-(4) \pm \sqrt{(4)^2 - 4\cdot(9)\cdot(-6)}}{2\cdot(9)}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant). (4)2−4⋅(9)⋅(−6)=16+216=232\sqrt{(4)^2 - 4\cdot(9)\cdot(-6)} = \sqrt{16 + 216} = \sqrt{232}
  4. Continue simplifying formula: Continue simplifying the quadratic formula with the calculated discriminant. f=−4±23218f = \frac{-4 \pm \sqrt{232}}{18}
  5. Identify possible values: Identify the two possible values for ff by considering both the positive and negative square roots.f=−4+23218f = \frac{{-4 + \sqrt{232}}}{{18}} or f=−4−23218f = \frac{{-4 - \sqrt{232}}}{{18}}
  6. Round values if necessary: Round the values of ff to the nearest hundredth, if necessary.f \approx (\-4 + 15.23) / 18 or f \approx (\-4 - 15.23) / 18f≈11.23/18f \approx 11.23 / 18 or f \approx \-19.23 / 18f≈0.62f \approx 0.62 or f \approx \-1.07

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