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Simplifying -36 = -34d + -16d2 Solving -36 = -34d + -16d2 Solving for variable 'd'. Reorder the terms: -36 + 34d + 16d2 = -34d + 34d + -16d2 + 16d2 Combine like terms: -34d + 34d = 0 -36 + 34d + 16d2 = 0 + -16d2 + 16d2 -36 + 34d + 16d2 = -16d2 + 16d2 Combine like terms: -16d2 + 16d2 = 0 -36 + 34d + 16d2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + 17d + 8d2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + 17d + 8d2)' equal to zero and attempt to solve: Simplifying -18 + 17d + 8d2 = 0 Solving -18 + 17d + 8d2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.25 + 2.125d + d2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 2.125d + 2.25 + d2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 2.125d + d2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 2.125d + d2 = 0 + 2.25 2.125d + d2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 2.125d + d2 = 2.25 The d term is 2.125d. Take half its coefficient (1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. 2.125d + 1.12890625 + d2 = 2.25 + 1.12890625 Reorder the terms: 1.12890625 + 2.125d + d2 = 2.25 + 1.12890625 Combine like terms: 2.25 + 1.12890625 = 3.37890625 1.12890625 + 2.125d + d2 = 3.37890625 Factor a perfect square on the left side: (d + 1.0625)(d + 1.0625) = 3.37890625 Calculate the square root of the right side: 1.838180146 Break this problem into two subproblems by setting (d + 1.0625) equal to 1.838180146 and -1.838180146.Subproblem 1
d + 1.0625 = 1.838180146 Simplifying d + 1.0625 = 1.838180146 Reorder the terms: 1.0625 + d = 1.838180146 Solving 1.0625 + d = 1.838180146 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1.0625' to each side of the equation. 1.0625 + -1.0625 + d = 1.838180146 + -1.0625 Combine like terms: 1.0625 + -1.0625 = 0.0000 0.0000 + d = 1.838180146 + -1.0625 d = 1.838180146 + -1.0625 Combine like terms: 1.838180146 + -1.0625 = 0.775680146 d = 0.775680146 Simplifying d = 0.775680146Subproblem 2
d + 1.0625 = -1.838180146 Simplifying d + 1.0625 = -1.838180146 Reorder the terms: 1.0625 + d = -1.838180146 Solving 1.0625 + d = -1.838180146 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1.0625' to each side of the equation. 1.0625 + -1.0625 + d = -1.838180146 + -1.0625 Combine like terms: 1.0625 + -1.0625 = 0.0000 0.0000 + d = -1.838180146 + -1.0625 d = -1.838180146 + -1.0625 Combine like terms: -1.838180146 + -1.0625 = -2.900680146 d = -2.900680146 Simplifying d = -2.900680146Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.775680146, -2.900680146}Solution
d = {0.775680146, -2.900680146}
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