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9s2+6s+1=09s^2 + 6s + 1 = 0

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Full solution

Q. 9s2+6s+1=09s^2 + 6s + 1 = 0
  1. Identify Quadratic Equation: Identify the quadratic equation to solve: 9s2+6s+1=09s^2 + 6s + 1 = 0.
  2. Use Quadratic Formula: Use the quadratic formula, s=−b±b2−4ac2as = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where a=9a = 9, b=6b = 6, and c=1c = 1.
  3. Calculate Discriminant: Calculate the discriminant, Δ=b2−4ac=(6)2−4(9)(1)=36−36=0\Delta = b^2 - 4ac = (6)^2 - 4(9)(1) = 36 - 36 = 0.
  4. Find Real Root: Since the discriminant Δ=0\Delta = 0, there is one real root, s=−b2as = -\frac{b}{2a}.
  5. Substitute Values: Substitute aa and bb into the formula: s=−6/(2⋅9)=−6/18=−1/3s = -6 / (2\cdot9) = -6 / 18 = -1/3.

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