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Simplifying d2 + 20d + 200 = 289 Reorder the terms: 200 + 20d + d2 = 289 Solving 200 + 20d + d2 = 289 Solving for variable 'd'. Reorder the terms: 200 + -289 + 20d + d2 = 289 + -289 Combine like terms: 200 + -289 = -89 -89 + 20d + d2 = 289 + -289 Combine like terms: 289 + -289 = 0 -89 + 20d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '89' to each side of the equation. -89 + 20d + 89 + d2 = 0 + 89 Reorder the terms: -89 + 89 + 20d + d2 = 0 + 89 Combine like terms: -89 + 89 = 0 0 + 20d + d2 = 0 + 89 20d + d2 = 0 + 89 Combine like terms: 0 + 89 = 89 20d + d2 = 89 The d term is 20d. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20d + 100 + d2 = 89 + 100 Reorder the terms: 100 + 20d + d2 = 89 + 100 Combine like terms: 89 + 100 = 189 100 + 20d + d2 = 189 Factor a perfect square on the left side: (d + 10)(d + 10) = 189 Calculate the square root of the right side: 13.747727085 Break this problem into two subproblems by setting (d + 10) equal to 13.747727085 and -13.747727085.Subproblem 1
d + 10 = 13.747727085 Simplifying d + 10 = 13.747727085 Reorder the terms: 10 + d = 13.747727085 Solving 10 + d = 13.747727085 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + d = 13.747727085 + -10 Combine like terms: 10 + -10 = 0 0 + d = 13.747727085 + -10 d = 13.747727085 + -10 Combine like terms: 13.747727085 + -10 = 3.747727085 d = 3.747727085 Simplifying d = 3.747727085Subproblem 2
d + 10 = -13.747727085 Simplifying d + 10 = -13.747727085 Reorder the terms: 10 + d = -13.747727085 Solving 10 + d = -13.747727085 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + d = -13.747727085 + -10 Combine like terms: 10 + -10 = 0 0 + d = -13.747727085 + -10 d = -13.747727085 + -10 Combine like terms: -13.747727085 + -10 = -23.747727085 d = -23.747727085 Simplifying d = -23.747727085Solution
The solution to the problem is based on the solutions from the subproblems. d = {3.747727085, -23.747727085}
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