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Simplifying 0 = 4d2 + 29d + -60 Reorder the terms: 0 = -60 + 29d + 4d2 Solving 0 = -60 + 29d + 4d2 Solving for variable 'd'. Combine like terms: 0 + 60 = 60 60 + -29d + -4d2 = -60 + 29d + 4d2 + 60 + -29d + -4d2 Reorder the terms: 60 + -29d + -4d2 = -60 + 60 + 29d + -29d + 4d2 + -4d2 Combine like terms: -60 + 60 = 0 60 + -29d + -4d2 = 0 + 29d + -29d + 4d2 + -4d2 60 + -29d + -4d2 = 29d + -29d + 4d2 + -4d2 Combine like terms: 29d + -29d = 0 60 + -29d + -4d2 = 0 + 4d2 + -4d2 60 + -29d + -4d2 = 4d2 + -4d2 Combine like terms: 4d2 + -4d2 = 0 60 + -29d + -4d2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -15 + 7.25d + d2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 7.25d + 15 + d2 = 0 + 15 Reorder the terms: -15 + 15 + 7.25d + d2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 7.25d + d2 = 0 + 15 7.25d + d2 = 0 + 15 Combine like terms: 0 + 15 = 15 7.25d + d2 = 15 The d term is 7.25d. Take half its coefficient (3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. 7.25d + 13.140625 + d2 = 15 + 13.140625 Reorder the terms: 13.140625 + 7.25d + d2 = 15 + 13.140625 Combine like terms: 15 + 13.140625 = 28.140625 13.140625 + 7.25d + d2 = 28.140625 Factor a perfect square on the left side: (d + 3.625)(d + 3.625) = 28.140625 Calculate the square root of the right side: 5.304773793 Break this problem into two subproblems by setting (d + 3.625) equal to 5.304773793 and -5.304773793.Subproblem 1
d + 3.625 = 5.304773793 Simplifying d + 3.625 = 5.304773793 Reorder the terms: 3.625 + d = 5.304773793 Solving 3.625 + d = 5.304773793 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + d = 5.304773793 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + d = 5.304773793 + -3.625 d = 5.304773793 + -3.625 Combine like terms: 5.304773793 + -3.625 = 1.679773793 d = 1.679773793 Simplifying d = 1.679773793Subproblem 2
d + 3.625 = -5.304773793 Simplifying d + 3.625 = -5.304773793 Reorder the terms: 3.625 + d = -5.304773793 Solving 3.625 + d = -5.304773793 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + d = -5.304773793 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + d = -5.304773793 + -3.625 d = -5.304773793 + -3.625 Combine like terms: -5.304773793 + -3.625 = -8.929773793 d = -8.929773793 Simplifying d = -8.929773793Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.679773793, -8.929773793}
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