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Solve using the quadratic formula.\newlinep2+6p+9=0p^2 + 6p + 9 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinep=p = _____ or p=p = _____

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Q. Solve using the quadratic formula.\newlinep2+6p+9=0p^2 + 6p + 9 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinep=p = _____ or p=p = _____
  1. Quadratic Formula Explanation: The quadratic formula is given by p=−b±b2−4ac2ap = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients from the quadratic equation ap2+bp+c=0ap^2 + bp + 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 p=−b/(2a)p = -b / (2a).
  5. Substitute Values: Substitute the values of bb and aa into the formula: p=−6/(2⋅1)=−6/2=−3p = -6 / (2\cdot1) = -6 / 2 = -3.
  6. Final Solution: The solution to the equation p2+6p+9=0p^2 + 6p + 9 = 0 is p=−3p = -3. Since the discriminant was 00, this is the only solution.

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