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Simplifying 6d2 + 21d = 10d + 36 Reorder the terms: 21d + 6d2 = 10d + 36 Reorder the terms: 21d + 6d2 = 36 + 10d Solving 21d + 6d2 = 36 + 10d Solving for variable 'd'. Reorder the terms: -36 + 21d + -10d + 6d2 = 36 + 10d + -36 + -10d Combine like terms: 21d + -10d = 11d -36 + 11d + 6d2 = 36 + 10d + -36 + -10d Reorder the terms: -36 + 11d + 6d2 = 36 + -36 + 10d + -10d Combine like terms: 36 + -36 = 0 -36 + 11d + 6d2 = 0 + 10d + -10d -36 + 11d + 6d2 = 10d + -10d Combine like terms: 10d + -10d = 0 -36 + 11d + 6d2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -6 + 1.833333333d + d2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 1.833333333d + 6 + d2 = 0 + 6 Reorder the terms: -6 + 6 + 1.833333333d + d2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 1.833333333d + d2 = 0 + 6 1.833333333d + d2 = 0 + 6 Combine like terms: 0 + 6 = 6 1.833333333d + d2 = 6 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 = 6 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333d + d2 = 6 + 0.8402777775 Combine like terms: 6 + 0.8402777775 = 6.8402777775 0.8402777775 + 1.833333333d + d2 = 6.8402777775 Factor a perfect square on the left side: (d + 0.9166666665)(d + 0.9166666665) = 6.8402777775 Calculate the square root of the right side: 2.615392471 Break this problem into two subproblems by setting (d + 0.9166666665) equal to 2.615392471 and -2.615392471.Subproblem 1
d + 0.9166666665 = 2.615392471 Simplifying d + 0.9166666665 = 2.615392471 Reorder the terms: 0.9166666665 + d = 2.615392471 Solving 0.9166666665 + d = 2.615392471 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 = 2.615392471 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + d = 2.615392471 + -0.9166666665 d = 2.615392471 + -0.9166666665 Combine like terms: 2.615392471 + -0.9166666665 = 1.6987258045 d = 1.6987258045 Simplifying d = 1.6987258045Subproblem 2
d + 0.9166666665 = -2.615392471 Simplifying d + 0.9166666665 = -2.615392471 Reorder the terms: 0.9166666665 + d = -2.615392471 Solving 0.9166666665 + d = -2.615392471 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 = -2.615392471 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + d = -2.615392471 + -0.9166666665 d = -2.615392471 + -0.9166666665 Combine like terms: -2.615392471 + -0.9166666665 = -3.5320591375 d = -3.5320591375 Simplifying d = -3.5320591375Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.6987258045, -3.5320591375}
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