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Solve using the quadratic formula.\newline3f2+6f+3=03f^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.\newline3f2+6f+3=03f^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 coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation 3f2+6f+3=03f^2 + 6f + 3 = 0.a=3a = 3, b=6b = 6, c=3c = 3
  2. Write quadratic formula: Write down the quadratic formula: f=−b±b2−4ac2af = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula.f=−(6)±(6)2−4⋅3⋅32⋅3f = \frac{{-(6) \pm \sqrt{{(6)^2 - 4\cdot3\cdot3}}}}{{2\cdot3}}
  4. Simplify discriminant: Simplify the expression under the square root (the discriminant). (6)2−4⋅3⋅3=36−36=0\sqrt{(6)^2 - 4\cdot 3\cdot 3} = \sqrt{36 - 36} = \sqrt{0}
  5. Find real solution: Since the discriminant is 00, there is only one real solution.f=−6±06f = \frac{{-6 \pm 0}}{{6}}
  6. Simplify expression: Simplify the expression to find the value of ff.f=(−6)/6f = (-6) / 6f=−1f = -1

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