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Solve using the quadratic formula.\newline9k2+6k+1=09k^2 + 6k + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinek=k = _____ or k=k = _____

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Q. Solve using the quadratic formula.\newline9k2+6k+1=09k^2 + 6k + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinek=k = _____ or k=k = _____
  1. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation 9k2+6k+1=09k^2 + 6k + 1 = 0.a=9a = 9, b=6b = 6, c=1c = 1.
  2. Write quadratic formula: Write down the quadratic formula: k=−b±b2−4ac2ak = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula.k=−(6)±(6)2−4(9)(1)2(9).k = \frac{{-(6) \pm \sqrt{{(6)^2 - 4(9)(1)}}}}{{2(9)}}.
  4. Simplify discriminant: Simplify the expression under the square root (the discriminant). (6)2−4(9)(1)=36−36=0\sqrt{(6)^2 - 4(9)(1)} = \sqrt{36 - 36} = \sqrt{0}.
  5. Find real solution: Since the discriminant is 00, there is only one real solution.\newlinek=(−6±0)/18k = (-6 \pm 0) / 18.
  6. Simplify expression: Simplify the expression to find the value of kk.k=−618=−13k = \frac{-6}{18} = -\frac{1}{3}.

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