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Simplifying -1.2d2 + 12.5d = 21.77 Reorder the terms: 12.5d + -1.2d2 = 21.77 Solving 12.5d + -1.2d2 = 21.77 Solving for variable 'd'. Reorder the terms: -21.77 + 12.5d + -1.2d2 = 21.77 + -21.77 Combine like terms: 21.77 + -21.77 = 0.00 -21.77 + 12.5d + -1.2d2 = 0.00 Begin completing the square. Divide all terms by -1.2 the coefficient of the squared term: Divide each side by '-1.2'. 18.14166667 + -10.41666667d + d2 = 0.0 Move the constant term to the right: Add '-18.14166667' to each side of the equation. 18.14166667 + -10.41666667d + -18.14166667 + d2 = 0.0 + -18.14166667 Reorder the terms: 18.14166667 + -18.14166667 + -10.41666667d + d2 = 0.0 + -18.14166667 Combine like terms: 18.14166667 + -18.14166667 = 0.00000000 0.00000000 + -10.41666667d + d2 = 0.0 + -18.14166667 -10.41666667d + d2 = 0.0 + -18.14166667 Combine like terms: 0.0 + -18.14166667 = -18.14166667 -10.41666667d + d2 = -18.14166667 The d term is -10.41666667d. Take half its coefficient (-5.208333335). Square it (27.12673613) and add it to both sides. Add '27.12673613' to each side of the equation. -10.41666667d + 27.12673613 + d2 = -18.14166667 + 27.12673613 Reorder the terms: 27.12673613 + -10.41666667d + d2 = -18.14166667 + 27.12673613 Combine like terms: -18.14166667 + 27.12673613 = 8.98506946 27.12673613 + -10.41666667d + d2 = 8.98506946 Factor a perfect square on the left side: (d + -5.208333335)(d + -5.208333335) = 8.98506946 Calculate the square root of the right side: 2.997510544 Break this problem into two subproblems by setting (d + -5.208333335) equal to 2.997510544 and -2.997510544.Subproblem 1
d + -5.208333335 = 2.997510544 Simplifying d + -5.208333335 = 2.997510544 Reorder the terms: -5.208333335 + d = 2.997510544 Solving -5.208333335 + d = 2.997510544 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '5.208333335' to each side of the equation. -5.208333335 + 5.208333335 + d = 2.997510544 + 5.208333335 Combine like terms: -5.208333335 + 5.208333335 = 0.000000000 0.000000000 + d = 2.997510544 + 5.208333335 d = 2.997510544 + 5.208333335 Combine like terms: 2.997510544 + 5.208333335 = 8.205843879 d = 8.205843879 Simplifying d = 8.205843879Subproblem 2
d + -5.208333335 = -2.997510544 Simplifying d + -5.208333335 = -2.997510544 Reorder the terms: -5.208333335 + d = -2.997510544 Solving -5.208333335 + d = -2.997510544 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '5.208333335' to each side of the equation. -5.208333335 + 5.208333335 + d = -2.997510544 + 5.208333335 Combine like terms: -5.208333335 + 5.208333335 = 0.000000000 0.000000000 + d = -2.997510544 + 5.208333335 d = -2.997510544 + 5.208333335 Combine like terms: -2.997510544 + 5.208333335 = 2.210822791 d = 2.210822791 Simplifying d = 2.210822791Solution
The solution to the problem is based on the solutions from the subproblems. d = {8.205843879, 2.210822791}
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