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Simplifying d2 + 16d = -9 Reorder the terms: 16d + d2 = -9 Solving 16d + d2 = -9 Solving for variable 'd'. Reorder the terms: 9 + 16d + d2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + 16d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 16d + -9 + d2 = 0 + -9 Reorder the terms: 9 + -9 + 16d + d2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 16d + d2 = 0 + -9 16d + d2 = 0 + -9 Combine like terms: 0 + -9 = -9 16d + d2 = -9 The d term is 16d. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16d + 64 + d2 = -9 + 64 Reorder the terms: 64 + 16d + d2 = -9 + 64 Combine like terms: -9 + 64 = 55 64 + 16d + d2 = 55 Factor a perfect square on the left side: (d + 8)(d + 8) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (d + 8) equal to 7.416198487 and -7.416198487.Subproblem 1
d + 8 = 7.416198487 Simplifying d + 8 = 7.416198487 Reorder the terms: 8 + d = 7.416198487 Solving 8 + d = 7.416198487 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + d = 7.416198487 + -8 Combine like terms: 8 + -8 = 0 0 + d = 7.416198487 + -8 d = 7.416198487 + -8 Combine like terms: 7.416198487 + -8 = -0.583801513 d = -0.583801513 Simplifying d = -0.583801513Subproblem 2
d + 8 = -7.416198487 Simplifying d + 8 = -7.416198487 Reorder the terms: 8 + d = -7.416198487 Solving 8 + d = -7.416198487 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + d = -7.416198487 + -8 Combine like terms: 8 + -8 = 0 0 + d = -7.416198487 + -8 d = -7.416198487 + -8 Combine like terms: -7.416198487 + -8 = -15.416198487 d = -15.416198487 Simplifying d = -15.416198487Solution
The solution to the problem is based on the solutions from the subproblems. d = {-0.583801513, -15.416198487}
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