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Solve using the quadratic formula.\newlined2+4d−5=0d^2 + 4d - 5 = 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−5=0d^2 + 4d - 5 = 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: Identify the values of aa, bb, and cc in the quadratic equation d2+4d−5=0d^2 + 4d − 5 = 0. The standard form of a quadratic equation is ax2+bx+c=0ax^2 + bx + c = 0. Comparing this with our equation, we get: a=1a = 1 b=4b = 4 c=−5c = -5
  2. Substitute values: 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}. Substituting the values we get: d=−(4)±(4)2−4⋅(1)⋅(−5)2⋅(1)d = \frac{-(4) \pm \sqrt{(4)^2 - 4\cdot(1)\cdot(-5)}}{2\cdot(1)}
  3. Simplify expression: Simplify the expression under the square root and calculate its value. (4)2−4⋅(1)⋅(−5)=16+20=36\sqrt{(4)^2 - 4\cdot(1)\cdot(-5)} = \sqrt{16 + 20} = \sqrt{36}
  4. Continue with formula: Continue with the quadratic formula using the value from the square root.\newlined=(−4±36)/2d = (-4 \pm \sqrt{36}) / 2\newlineSince 36\sqrt{36} is 66, we have:\newlined=(−4±6)/2d = (-4 \pm 6) / 2
  5. Find possible values: Find the two possible values for dd.d=−4+62d = \frac{{-4 + 6}}{{2}} or d=−4−62d = \frac{{-4 - 6}}{{2}}d=22d = \frac{{2}}{{2}} or d=−102d = \frac{{-10}}{{2}}d=1d = 1 or d=−5d = -5

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