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Solve using the quadratic formula.\newlined2+d−6=0d^2 + d - 6 = 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+d−6=0d^2 + d - 6 = 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+d−6=0d^2 + d − 6 = 0. Compare d2+d−6=0d^2 + d − 6 = 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. The quadratic formula is d=−b±b2−4ac2ad = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. So we have: d=−(1)±(1)2−4⋅1⋅(−6)2⋅1d = \frac{-(1) \pm \sqrt{(1)^2 - 4\cdot1\cdot(-6)}}{2\cdot1}
  3. Simplify expression under square root: Simplify the expression under the square root. (1)2−4⋅1⋅(−6)\sqrt{(1)^2 - 4\cdot 1\cdot (-6)} = 1+24\sqrt{1 + 24} = 25\sqrt{25}
  4. Continue simplifying quadratic formula: Continue simplifying the quadratic formula with the value from Step 33.\newlined=−1±252d = \frac{-1 \pm \sqrt{25}}{2}\newlineSince 25=5\sqrt{25} = 5, we have:\newlined=−1±52d = \frac{-1 \pm 5}{2}
  5. Find two possible values for \newlinedd: Find the two possible values for \newlinedd.\newline\newlined=(−1+5)/2d = (-1 + 5) / 2 or \newlined=(−1−5)/2d = (-1 - 5) / 2\newline\newlined=4/2d = 4 / 2 or \newlined=−6/2d = -6 / 2\newline\newlined=2d = 2 or \newlined=−3d = -3

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