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Simplifying 36 = 48d + -1d2 Solving 36 = 48d + -1d2 Solving for variable 'd'. Reorder the terms: 36 + -48d + d2 = 48d + -48d + -1d2 + d2 Combine like terms: 48d + -48d = 0 36 + -48d + d2 = 0 + -1d2 + d2 36 + -48d + d2 = -1d2 + d2 Combine like terms: -1d2 + d2 = 0 36 + -48d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -48d + -36 + d2 = 0 + -36 Reorder the terms: 36 + -36 + -48d + d2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -48d + d2 = 0 + -36 -48d + d2 = 0 + -36 Combine like terms: 0 + -36 = -36 -48d + d2 = -36 The d term is -48d. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48d + 576 + d2 = -36 + 576 Reorder the terms: 576 + -48d + d2 = -36 + 576 Combine like terms: -36 + 576 = 540 576 + -48d + d2 = 540 Factor a perfect square on the left side: (d + -24)(d + -24) = 540 Calculate the square root of the right side: 23.237900077 Break this problem into two subproblems by setting (d + -24) equal to 23.237900077 and -23.237900077.Subproblem 1
d + -24 = 23.237900077 Simplifying d + -24 = 23.237900077 Reorder the terms: -24 + d = 23.237900077 Solving -24 + d = 23.237900077 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + d = 23.237900077 + 24 Combine like terms: -24 + 24 = 0 0 + d = 23.237900077 + 24 d = 23.237900077 + 24 Combine like terms: 23.237900077 + 24 = 47.237900077 d = 47.237900077 Simplifying d = 47.237900077Subproblem 2
d + -24 = -23.237900077 Simplifying d + -24 = -23.237900077 Reorder the terms: -24 + d = -23.237900077 Solving -24 + d = -23.237900077 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + d = -23.237900077 + 24 Combine like terms: -24 + 24 = 0 0 + d = -23.237900077 + 24 d = -23.237900077 + 24 Combine like terms: -23.237900077 + 24 = 0.762099923 d = 0.762099923 Simplifying d = 0.762099923Solution
The solution to the problem is based on the solutions from the subproblems. d = {47.237900077, 0.762099923}
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