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Solve using the quadratic formula.\newline3x2+6x+3=03x^2 + 6x + 3 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinex=x = _____ or x=x = _____

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Q. Solve using the quadratic formula.\newline3x2+6x+3=03x^2 + 6x + 3 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinex=x = _____ or x=x = _____
  1. Quadratic Formula Definition: The quadratic formula is given by x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients of the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0. In this case, a=3a = 3, b=6b = 6, and c=3c = 3.
  2. Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac. For our equation, the discriminant is 62−4(3)(3)6^2 - 4(3)(3).
  3. Discriminant Calculation: Perform the calculation: 62−4(3)(3)=36−36=06^2 - 4(3)(3) = 36 - 36 = 0.
  4. One Real Solution: Since the discriminant is 00, there is only one real solution to the equation, and it is not necessary to calculate the ±\pm part of the formula. We can proceed with x=−b/(2a)x = -b / (2a).
  5. Substitute Values: Substitute the values of aa and bb into the formula: x=−6(2×3)x = \frac{-6}{(2 \times 3)}.
  6. Final Calculation: Perform the calculation: x=−6/6=−1x = -6 / 6 = -1.
  7. Unique Solution: The solution to the equation 3x2+6x+3=03x^2 + 6x + 3 = 0 is x=−1x = -1. Since the discriminant was 00, there is only one unique solution.

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