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Solve using the quadratic formula.\newlined2+2d+1=0d^2 + 2d + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlined=d = _____ or d=d = _____

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Q. Solve using the quadratic formula.\newlined2+2d+1=0d^2 + 2d + 1 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlined=d = _____ or d=d = _____
  1. Identify coefficients: Identify the coefficients of the quadratic equation d2+2d+1=0d^2 + 2d + 1 = 0. The standard form of a quadratic equation is ax2+bx+c=0ax^2 + bx + c = 0. Here, a=1a = 1, b=2b = 2, and c=1c = 1.
  2. Recall quadratic formula: Recall the quadratic formula, which is d=−b±b2−4ac2ad = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. We will use this formula to find the values of dd.
  3. Substitute coefficients: Substitute the coefficients aa, bb, and cc into the quadratic formula. This gives us d=(−(2)±(2)2−4(1)(1))/(2(1))d = (-(2) \pm \sqrt{(2)^2 - 4(1)(1)}) / (2(1)).
  4. Simplify equation: Simplify the equation step by step. First, calculate the discriminant b2−4acb^2 - 4ac: (2)2−4(1)(1)=4−4=0(2)^2 - 4(1)(1) = 4 - 4 = 0.
  5. Calculate discriminant: Since the discriminant is 00, there is only one real solution. Continue simplifying: d=(−2±0)/2d = (-2 \pm \sqrt{0}) / 2.
  6. Find real solution: The square root of 00 is 00, so the equation simplifies to d=(−2+0)/2d = (-2 + 0) / 2 or d=(−2−0)/2d = (-2 - 0) / 2, which both yield the same result.
  7. Divide to get result: Divide −2-2 by 22 to get the solution for dd. This gives us d=−1d = -1.

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