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Simplifying d2 + 10d + -684.5217391 = 0 Reorder the terms: -684.5217391 + 10d + d2 = 0 Solving -684.5217391 + 10d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '684.5217391' to each side of the equation. -684.5217391 + 10d + 684.5217391 + d2 = 0 + 684.5217391 Reorder the terms: -684.5217391 + 684.5217391 + 10d + d2 = 0 + 684.5217391 Combine like terms: -684.5217391 + 684.5217391 = 0.0000000 0.0000000 + 10d + d2 = 0 + 684.5217391 10d + d2 = 0 + 684.5217391 Combine like terms: 0 + 684.5217391 = 684.5217391 10d + d2 = 684.5217391 The d term is 10d. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10d + 25 + d2 = 684.5217391 + 25 Reorder the terms: 25 + 10d + d2 = 684.5217391 + 25 Combine like terms: 684.5217391 + 25 = 709.5217391 25 + 10d + d2 = 709.5217391 Factor a perfect square on the left side: (d + 5)(d + 5) = 709.5217391 Calculate the square root of the right side: 26.636849271 Break this problem into two subproblems by setting (d + 5) equal to 26.636849271 and -26.636849271.Subproblem 1
d + 5 = 26.636849271 Simplifying d + 5 = 26.636849271 Reorder the terms: 5 + d = 26.636849271 Solving 5 + d = 26.636849271 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + d = 26.636849271 + -5 Combine like terms: 5 + -5 = 0 0 + d = 26.636849271 + -5 d = 26.636849271 + -5 Combine like terms: 26.636849271 + -5 = 21.636849271 d = 21.636849271 Simplifying d = 21.636849271Subproblem 2
d + 5 = -26.636849271 Simplifying d + 5 = -26.636849271 Reorder the terms: 5 + d = -26.636849271 Solving 5 + d = -26.636849271 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + d = -26.636849271 + -5 Combine like terms: 5 + -5 = 0 0 + d = -26.636849271 + -5 d = -26.636849271 + -5 Combine like terms: -26.636849271 + -5 = -31.636849271 d = -31.636849271 Simplifying d = -31.636849271Solution
The solution to the problem is based on the solutions from the subproblems. d = {21.636849271, -31.636849271}
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