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Simplifying -6d2 + -2d + 6 = 0 Reorder the terms: 6 + -2d + -6d2 = 0 Solving 6 + -2d + -6d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -1d + -3d2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -1d + -3d2)' equal to zero and attempt to solve: Simplifying 3 + -1d + -3d2 = 0 Solving 3 + -1d + -3d2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1 + 0.3333333333d + d2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.3333333333d + 1 + d2 = 0 + 1 Reorder the terms: -1 + 1 + 0.3333333333d + d2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.3333333333d + d2 = 0 + 1 0.3333333333d + d2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.3333333333d + d2 = 1 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 = 1 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333d + d2 = 1 + 0.02777777779 Combine like terms: 1 + 0.02777777779 = 1.02777777779 0.02777777779 + 0.3333333333d + d2 = 1.02777777779 Factor a perfect square on the left side: (d + 0.1666666667)(d + 0.1666666667) = 1.02777777779 Calculate the square root of the right side: 1.013793755 Break this problem into two subproblems by setting (d + 0.1666666667) equal to 1.013793755 and -1.013793755.Subproblem 1
d + 0.1666666667 = 1.013793755 Simplifying d + 0.1666666667 = 1.013793755 Reorder the terms: 0.1666666667 + d = 1.013793755 Solving 0.1666666667 + d = 1.013793755 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + d = 1.013793755 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + d = 1.013793755 + -0.1666666667 d = 1.013793755 + -0.1666666667 Combine like terms: 1.013793755 + -0.1666666667 = 0.8471270883 d = 0.8471270883 Simplifying d = 0.8471270883Subproblem 2
d + 0.1666666667 = -1.013793755 Simplifying d + 0.1666666667 = -1.013793755 Reorder the terms: 0.1666666667 + d = -1.013793755 Solving 0.1666666667 + d = -1.013793755 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + d = -1.013793755 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + d = -1.013793755 + -0.1666666667 d = -1.013793755 + -0.1666666667 Combine like terms: -1.013793755 + -0.1666666667 = -1.1804604217 d = -1.1804604217 Simplifying d = -1.1804604217Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.8471270883, -1.1804604217}Solution
d = {0.8471270883, -1.1804604217}
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