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Solve using the quadratic formula.\newlined2−4d+2=0d^2 - 4d + 2 = 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.\newlined2−4d+2=0d^2 - 4d + 2 = 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 d2−4d+2=0d^2 − 4d + 2 = 0. Compare d2−4d+2=0d^2 − 4d + 2 = 0 with the standard form ax2+bx+c=0ax^2 + bx + c = 0. a=1a = 1 bb00 bb11
  2. Substitute values into quadratic formula: Substitute the values of aa, bb, and cc into the quadratic formula to find dd.d=−b±b2−4ac2ad = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}d=−(−4)±(−4)2−4⋅1⋅22⋅1d = \frac{-(-4) \pm \sqrt{(-4)^2 - 4\cdot1\cdot2}}{2\cdot1}
  3. Simplify expression and constants: Simplify the expression under the square root and the constants outside the square root. \newlined=4±16−82d = \frac{4 \pm \sqrt{16 - 8}}{2}\newlined=4±82d = \frac{4 \pm \sqrt{8}}{2}
  4. Simplify square root of 88: Simplify the square root of 88. 8\sqrt{8} can be simplified to 4×2\sqrt{4\times2}, which is 2×22\times\sqrt{2}. d=4±2×22d = \frac{4 \pm 2\times\sqrt{2}}{2}
  5. Divide terms by 22: Simplify the expression by dividing each term by 22.\newlined=2±22d = \frac{2 \pm \sqrt{2}}{2}
  6. Write final solutions for dd: Write the final solutions for dd.d=2+2d = 2 + \sqrt{2} or d=2−2d = 2 - \sqrt{2}Round the values of dd to the nearest hundredth, if necessary.d≈2+1.41d \approx 2 + 1.41 or d≈2−1.41d \approx 2 - 1.41d≈3.41d \approx 3.41 or d≈0.59d \approx 0.59

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