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Simplifying d2 + -29d = -33 Reorder the terms: -29d + d2 = -33 Solving -29d + d2 = -33 Solving for variable 'd'. Reorder the terms: 33 + -29d + d2 = -33 + 33 Combine like terms: -33 + 33 = 0 33 + -29d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-33' to each side of the equation. 33 + -29d + -33 + d2 = 0 + -33 Reorder the terms: 33 + -33 + -29d + d2 = 0 + -33 Combine like terms: 33 + -33 = 0 0 + -29d + d2 = 0 + -33 -29d + d2 = 0 + -33 Combine like terms: 0 + -33 = -33 -29d + d2 = -33 The d term is -29d. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29d + 210.25 + d2 = -33 + 210.25 Reorder the terms: 210.25 + -29d + d2 = -33 + 210.25 Combine like terms: -33 + 210.25 = 177.25 210.25 + -29d + d2 = 177.25 Factor a perfect square on the left side: (d + -14.5)(d + -14.5) = 177.25 Calculate the square root of the right side: 13.313526956 Break this problem into two subproblems by setting (d + -14.5) equal to 13.313526956 and -13.313526956.Subproblem 1
d + -14.5 = 13.313526956 Simplifying d + -14.5 = 13.313526956 Reorder the terms: -14.5 + d = 13.313526956 Solving -14.5 + d = 13.313526956 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + d = 13.313526956 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + d = 13.313526956 + 14.5 d = 13.313526956 + 14.5 Combine like terms: 13.313526956 + 14.5 = 27.813526956 d = 27.813526956 Simplifying d = 27.813526956Subproblem 2
d + -14.5 = -13.313526956 Simplifying d + -14.5 = -13.313526956 Reorder the terms: -14.5 + d = -13.313526956 Solving -14.5 + d = -13.313526956 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + d = -13.313526956 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + d = -13.313526956 + 14.5 d = -13.313526956 + 14.5 Combine like terms: -13.313526956 + 14.5 = 1.186473044 d = 1.186473044 Simplifying d = 1.186473044Solution
The solution to the problem is based on the solutions from the subproblems. d = {27.813526956, 1.186473044}
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