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Simplifying 0 = -0.01d2 + 1.06d + -18 Reorder the terms: 0 = -18 + 1.06d + -0.01d2 Solving 0 = -18 + 1.06d + -0.01d2 Solving for variable 'd'. Combine like terms: 0 + 18 = 18 18 + -1.06d + 0.01d2 = -18 + 1.06d + -0.01d2 + 18 + -1.06d + 0.01d2 Reorder the terms: 18 + -1.06d + 0.01d2 = -18 + 18 + 1.06d + -1.06d + -0.01d2 + 0.01d2 Combine like terms: -18 + 18 = 0 18 + -1.06d + 0.01d2 = 0 + 1.06d + -1.06d + -0.01d2 + 0.01d2 18 + -1.06d + 0.01d2 = 1.06d + -1.06d + -0.01d2 + 0.01d2 Combine like terms: 1.06d + -1.06d = 0.00 18 + -1.06d + 0.01d2 = 0.00 + -0.01d2 + 0.01d2 18 + -1.06d + 0.01d2 = -0.01d2 + 0.01d2 Combine like terms: -0.01d2 + 0.01d2 = 0.00 18 + -1.06d + 0.01d2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. 1800 + -106d + d2 = 0 Move the constant term to the right: Add '-1800' to each side of the equation. 1800 + -106d + -1800 + d2 = 0 + -1800 Reorder the terms: 1800 + -1800 + -106d + d2 = 0 + -1800 Combine like terms: 1800 + -1800 = 0 0 + -106d + d2 = 0 + -1800 -106d + d2 = 0 + -1800 Combine like terms: 0 + -1800 = -1800 -106d + d2 = -1800 The d term is -106d. Take half its coefficient (-53). Square it (2809) and add it to both sides. Add '2809' to each side of the equation. -106d + 2809 + d2 = -1800 + 2809 Reorder the terms: 2809 + -106d + d2 = -1800 + 2809 Combine like terms: -1800 + 2809 = 1009 2809 + -106d + d2 = 1009 Factor a perfect square on the left side: (d + -53)(d + -53) = 1009 Calculate the square root of the right side: 31.764760349 Break this problem into two subproblems by setting (d + -53) equal to 31.764760349 and -31.764760349.Subproblem 1
d + -53 = 31.764760349 Simplifying d + -53 = 31.764760349 Reorder the terms: -53 + d = 31.764760349 Solving -53 + d = 31.764760349 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '53' to each side of the equation. -53 + 53 + d = 31.764760349 + 53 Combine like terms: -53 + 53 = 0 0 + d = 31.764760349 + 53 d = 31.764760349 + 53 Combine like terms: 31.764760349 + 53 = 84.764760349 d = 84.764760349 Simplifying d = 84.764760349Subproblem 2
d + -53 = -31.764760349 Simplifying d + -53 = -31.764760349 Reorder the terms: -53 + d = -31.764760349 Solving -53 + d = -31.764760349 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '53' to each side of the equation. -53 + 53 + d = -31.764760349 + 53 Combine like terms: -53 + 53 = 0 0 + d = -31.764760349 + 53 d = -31.764760349 + 53 Combine like terms: -31.764760349 + 53 = 21.235239651 d = 21.235239651 Simplifying d = 21.235239651Solution
The solution to the problem is based on the solutions from the subproblems. d = {84.764760349, 21.235239651}
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