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Simplifying 0 = d2 + 17d + -30 Reorder the terms: 0 = -30 + 17d + d2 Solving 0 = -30 + 17d + d2 Solving for variable 'd'. Combine like terms: 0 + 30 = 30 30 + -17d + -1d2 = -30 + 17d + d2 + 30 + -17d + -1d2 Reorder the terms: 30 + -17d + -1d2 = -30 + 30 + 17d + -17d + d2 + -1d2 Combine like terms: -30 + 30 = 0 30 + -17d + -1d2 = 0 + 17d + -17d + d2 + -1d2 30 + -17d + -1d2 = 17d + -17d + d2 + -1d2 Combine like terms: 17d + -17d = 0 30 + -17d + -1d2 = 0 + d2 + -1d2 30 + -17d + -1d2 = d2 + -1d2 Combine like terms: d2 + -1d2 = 0 30 + -17d + -1d2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -30 + 17d + d2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 17d + 30 + d2 = 0 + 30 Reorder the terms: -30 + 30 + 17d + d2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 17d + d2 = 0 + 30 17d + d2 = 0 + 30 Combine like terms: 0 + 30 = 30 17d + d2 = 30 The d term is 17d. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17d + 72.25 + d2 = 30 + 72.25 Reorder the terms: 72.25 + 17d + d2 = 30 + 72.25 Combine like terms: 30 + 72.25 = 102.25 72.25 + 17d + d2 = 102.25 Factor a perfect square on the left side: (d + 8.5)(d + 8.5) = 102.25 Calculate the square root of the right side: 10.111874208 Break this problem into two subproblems by setting (d + 8.5) equal to 10.111874208 and -10.111874208.Subproblem 1
d + 8.5 = 10.111874208 Simplifying d + 8.5 = 10.111874208 Reorder the terms: 8.5 + d = 10.111874208 Solving 8.5 + d = 10.111874208 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + d = 10.111874208 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + d = 10.111874208 + -8.5 d = 10.111874208 + -8.5 Combine like terms: 10.111874208 + -8.5 = 1.611874208 d = 1.611874208 Simplifying d = 1.611874208Subproblem 2
d + 8.5 = -10.111874208 Simplifying d + 8.5 = -10.111874208 Reorder the terms: 8.5 + d = -10.111874208 Solving 8.5 + d = -10.111874208 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + d = -10.111874208 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + d = -10.111874208 + -8.5 d = -10.111874208 + -8.5 Combine like terms: -10.111874208 + -8.5 = -18.611874208 d = -18.611874208 Simplifying d = -18.611874208Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.611874208, -18.611874208}
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