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Simplifying -3d2 + 9d + -2 = 0 Reorder the terms: -2 + 9d + -3d2 = 0 Solving -2 + 9d + -3d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 0.6666666667 + -3d + d2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -3d + -0.6666666667 + d2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -3d + d2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -3d + d2 = 0 + -0.6666666667 -3d + d2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -3d + d2 = -0.6666666667 The d term is -3d. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3d + 2.25 + d2 = -0.6666666667 + 2.25 Reorder the terms: 2.25 + -3d + d2 = -0.6666666667 + 2.25 Combine like terms: -0.6666666667 + 2.25 = 1.5833333333 2.25 + -3d + d2 = 1.5833333333 Factor a perfect square on the left side: (d + -1.5)(d + -1.5) = 1.5833333333 Calculate the square root of the right side: 1.258305739 Break this problem into two subproblems by setting (d + -1.5) equal to 1.258305739 and -1.258305739.Subproblem 1
d + -1.5 = 1.258305739 Simplifying d + -1.5 = 1.258305739 Reorder the terms: -1.5 + d = 1.258305739 Solving -1.5 + d = 1.258305739 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + d = 1.258305739 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + d = 1.258305739 + 1.5 d = 1.258305739 + 1.5 Combine like terms: 1.258305739 + 1.5 = 2.758305739 d = 2.758305739 Simplifying d = 2.758305739Subproblem 2
d + -1.5 = -1.258305739 Simplifying d + -1.5 = -1.258305739 Reorder the terms: -1.5 + d = -1.258305739 Solving -1.5 + d = -1.258305739 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + d = -1.258305739 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + d = -1.258305739 + 1.5 d = -1.258305739 + 1.5 Combine like terms: -1.258305739 + 1.5 = 0.241694261 d = 0.241694261 Simplifying d = 0.241694261Solution
The solution to the problem is based on the solutions from the subproblems. d = {2.758305739, 0.241694261}
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