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Solve using the quadratic formula.\newline2d2+8d+8=02d^2 + 8d + 8 = 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.\newline2d2+8d+8=02d^2 + 8d + 8 = 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 values of aa, bb, cc: Identify the values of aa, bb, and cc in the quadratic equation 2d2+8d+8=02d^2 + 8d + 8 = 0. By comparing the equation with the standard form ax2+bx+c=0ax^2 + bx + c = 0, we find: a=2a = 2 b=8b = 8 bb00
  2. Substitute values into formula: Substitute the values of aa, bb, and cc into the quadratic formula to find dd. The quadratic formula is d=−b±b2−4ac2ad = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. So we have: d=−(8)±(8)2−4⋅2⋅82⋅2d = \frac{-(8) \pm \sqrt{(8)^2 - 4\cdot2\cdot8}}{2\cdot2}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant). (8)2−4⋅2⋅8=64−64=0\sqrt{(8)^2 - 4\cdot 2\cdot 8} = \sqrt{64 - 64} = \sqrt{0}
  4. Continue simplifying formula: Continue simplifying the quadratic formula with the calculated discriminant.\newlined=−8±04d = \frac{-8 \pm \sqrt{0}}{4}\newlineSince 0=0\sqrt{0} = 0, the equation simplifies to:\newlined=−8±04d = \frac{-8 \pm 0}{4}
  5. Solve for d: Solve for the two possible values of d.\newlineSince the discriminant is 00, there is only one real solution:\newlined=(−8+0)/4d = (-8 + 0) / 4 or d=(−8−0)/4d = (-8 - 0) / 4\newlineBoth expressions simplify to the same value:\newlined=−8/4d = -8 / 4\newlined=−2d = -2

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