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Simplifying d2 + 4d = 23 Reorder the terms: 4d + d2 = 23 Solving 4d + d2 = 23 Solving for variable 'd'. Reorder the terms: -23 + 4d + d2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + 4d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 4d + 23 + d2 = 0 + 23 Reorder the terms: -23 + 23 + 4d + d2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 4d + d2 = 0 + 23 4d + d2 = 0 + 23 Combine like terms: 0 + 23 = 23 4d + d2 = 23 The d term is 4d. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4d + 4 + d2 = 23 + 4 Reorder the terms: 4 + 4d + d2 = 23 + 4 Combine like terms: 23 + 4 = 27 4 + 4d + d2 = 27 Factor a perfect square on the left side: (d + 2)(d + 2) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (d + 2) equal to 5.196152423 and -5.196152423.Subproblem 1
d + 2 = 5.196152423 Simplifying d + 2 = 5.196152423 Reorder the terms: 2 + d = 5.196152423 Solving 2 + d = 5.196152423 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + d = 5.196152423 + -2 Combine like terms: 2 + -2 = 0 0 + d = 5.196152423 + -2 d = 5.196152423 + -2 Combine like terms: 5.196152423 + -2 = 3.196152423 d = 3.196152423 Simplifying d = 3.196152423Subproblem 2
d + 2 = -5.196152423 Simplifying d + 2 = -5.196152423 Reorder the terms: 2 + d = -5.196152423 Solving 2 + d = -5.196152423 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + d = -5.196152423 + -2 Combine like terms: 2 + -2 = 0 0 + d = -5.196152423 + -2 d = -5.196152423 + -2 Combine like terms: -5.196152423 + -2 = -7.196152423 d = -7.196152423 Simplifying d = -7.196152423Solution
The solution to the problem is based on the solutions from the subproblems. d = {3.196152423, -7.196152423}
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