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Simplifying -21d2 + -7d + -5 = 0 Reorder the terms: -5 + -7d + -21d2 = 0 Solving -5 + -7d + -21d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 7d + 21d2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 7d + 21d2)' equal to zero and attempt to solve: Simplifying 5 + 7d + 21d2 = 0 Solving 5 + 7d + 21d2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.2380952381 + 0.3333333333d + d2 = 0 Move the constant term to the right: Add '-0.2380952381' to each side of the equation. 0.2380952381 + 0.3333333333d + -0.2380952381 + d2 = 0 + -0.2380952381 Reorder the terms: 0.2380952381 + -0.2380952381 + 0.3333333333d + d2 = 0 + -0.2380952381 Combine like terms: 0.2380952381 + -0.2380952381 = 0.0000000000 0.0000000000 + 0.3333333333d + d2 = 0 + -0.2380952381 0.3333333333d + d2 = 0 + -0.2380952381 Combine like terms: 0 + -0.2380952381 = -0.2380952381 0.3333333333d + d2 = -0.2380952381 The d term is 0.3333333333d. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333d + 0.02777777779 + d2 = -0.2380952381 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333d + d2 = -0.2380952381 + 0.02777777779 Combine like terms: -0.2380952381 + 0.02777777779 = -0.21031746031 0.02777777779 + 0.3333333333d + d2 = -0.21031746031 Factor a perfect square on the left side: (d + 0.1666666667)(d + 0.1666666667) = -0.21031746031 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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