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Simplifying 0 = -0.01d2 + 1.06d + -22 Reorder the terms: 0 = -22 + 1.06d + -0.01d2 Solving 0 = -22 + 1.06d + -0.01d2 Solving for variable 'd'. Combine like terms: 0 + 22 = 22 22 + -1.06d + 0.01d2 = -22 + 1.06d + -0.01d2 + 22 + -1.06d + 0.01d2 Reorder the terms: 22 + -1.06d + 0.01d2 = -22 + 22 + 1.06d + -1.06d + -0.01d2 + 0.01d2 Combine like terms: -22 + 22 = 0 22 + -1.06d + 0.01d2 = 0 + 1.06d + -1.06d + -0.01d2 + 0.01d2 22 + -1.06d + 0.01d2 = 1.06d + -1.06d + -0.01d2 + 0.01d2 Combine like terms: 1.06d + -1.06d = 0.00 22 + -1.06d + 0.01d2 = 0.00 + -0.01d2 + 0.01d2 22 + -1.06d + 0.01d2 = -0.01d2 + 0.01d2 Combine like terms: -0.01d2 + 0.01d2 = 0.00 22 + -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'. 2200 + -106d + d2 = 0 Move the constant term to the right: Add '-2200' to each side of the equation. 2200 + -106d + -2200 + d2 = 0 + -2200 Reorder the terms: 2200 + -2200 + -106d + d2 = 0 + -2200 Combine like terms: 2200 + -2200 = 0 0 + -106d + d2 = 0 + -2200 -106d + d2 = 0 + -2200 Combine like terms: 0 + -2200 = -2200 -106d + d2 = -2200 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 = -2200 + 2809 Reorder the terms: 2809 + -106d + d2 = -2200 + 2809 Combine like terms: -2200 + 2809 = 609 2809 + -106d + d2 = 609 Factor a perfect square on the left side: (d + -53)(d + -53) = 609 Calculate the square root of the right side: 24.677925359 Break this problem into two subproblems by setting (d + -53) equal to 24.677925359 and -24.677925359.Subproblem 1
d + -53 = 24.677925359 Simplifying d + -53 = 24.677925359 Reorder the terms: -53 + d = 24.677925359 Solving -53 + d = 24.677925359 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 = 24.677925359 + 53 Combine like terms: -53 + 53 = 0 0 + d = 24.677925359 + 53 d = 24.677925359 + 53 Combine like terms: 24.677925359 + 53 = 77.677925359 d = 77.677925359 Simplifying d = 77.677925359Subproblem 2
d + -53 = -24.677925359 Simplifying d + -53 = -24.677925359 Reorder the terms: -53 + d = -24.677925359 Solving -53 + d = -24.677925359 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 = -24.677925359 + 53 Combine like terms: -53 + 53 = 0 0 + d = -24.677925359 + 53 d = -24.677925359 + 53 Combine like terms: -24.677925359 + 53 = 28.322074641 d = 28.322074641 Simplifying d = 28.322074641Solution
The solution to the problem is based on the solutions from the subproblems. d = {77.677925359, 28.322074641}
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