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Solve using the quadratic formula.\newliner2+6r+9=0r^2 + 6r + 9 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliner=r = _____ or r=r = _____

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Q. Solve using the quadratic formula.\newliner2+6r+9=0r^2 + 6r + 9 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliner=r = _____ or r=r = _____
  1. Quadratic Formula: The quadratic formula is given by r=−b±b2−4ac2ar = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients from the quadratic equation ar2+br+c=0ar^2 + br + c = 0. In this case, a=1a = 1, b=6b = 6, and c=9c = 9.
  2. Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac. Here, it is 62−4(1)(9)6^2 - 4(1)(9).
  3. Discriminant Calculation: Perform the calculation: 36−4(1)(9)=36−36=036 - 4(1)(9) = 36 - 36 = 0.
  4. Real Solution Determination: Since the discriminant is 00, there is only one real solution to the equation, and it is not necessary to use the ±\pm symbol in the quadratic formula. The solution is r=−b/(2a)r = -b / (2a).
  5. Substitute Values: Substitute the values of bb and aa into the formula: r=−6/(2⋅1)=−6/2r = -6 / (2\cdot1) = -6 / 2.
  6. Division Calculation: Perform the division to find the solution: r=−6/2=−3r = -6 / 2 = -3.

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