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Simplifying 6d2 + 11d + -3 = 0 Reorder the terms: -3 + 11d + 6d2 = 0 Solving -3 + 11d + 6d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + 1.833333333d + d2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 1.833333333d + 0.5 + d2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 1.833333333d + d2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 1.833333333d + d2 = 0 + 0.5 1.833333333d + d2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 1.833333333d + d2 = 0.5 The d term is 1.833333333d. Take half its coefficient (0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. 1.833333333d + 0.8402777775 + d2 = 0.5 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333d + d2 = 0.5 + 0.8402777775 Combine like terms: 0.5 + 0.8402777775 = 1.3402777775 0.8402777775 + 1.833333333d + d2 = 1.3402777775 Factor a perfect square on the left side: (d + 0.9166666665)(d + 0.9166666665) = 1.3402777775 Calculate the square root of the right side: 1.157703666 Break this problem into two subproblems by setting (d + 0.9166666665) equal to 1.157703666 and -1.157703666.Subproblem 1
d + 0.9166666665 = 1.157703666 Simplifying d + 0.9166666665 = 1.157703666 Reorder the terms: 0.9166666665 + d = 1.157703666 Solving 0.9166666665 + d = 1.157703666 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + d = 1.157703666 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + d = 1.157703666 + -0.9166666665 d = 1.157703666 + -0.9166666665 Combine like terms: 1.157703666 + -0.9166666665 = 0.2410369995 d = 0.2410369995 Simplifying d = 0.2410369995Subproblem 2
d + 0.9166666665 = -1.157703666 Simplifying d + 0.9166666665 = -1.157703666 Reorder the terms: 0.9166666665 + d = -1.157703666 Solving 0.9166666665 + d = -1.157703666 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + d = -1.157703666 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + d = -1.157703666 + -0.9166666665 d = -1.157703666 + -0.9166666665 Combine like terms: -1.157703666 + -0.9166666665 = -2.0743703325 d = -2.0743703325 Simplifying d = -2.0743703325Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.2410369995, -2.0743703325}
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