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Simplifying 188d + 157d2 = 500 Solving 188d + 157d2 = 500 Solving for variable 'd'. Reorder the terms: -500 + 188d + 157d2 = 500 + -500 Combine like terms: 500 + -500 = 0 -500 + 188d + 157d2 = 0 Begin completing the square. Divide all terms by 157 the coefficient of the squared term: Divide each side by '157'. -3.184713376 + 1.197452229d + d2 = 0 Move the constant term to the right: Add '3.184713376' to each side of the equation. -3.184713376 + 1.197452229d + 3.184713376 + d2 = 0 + 3.184713376 Reorder the terms: -3.184713376 + 3.184713376 + 1.197452229d + d2 = 0 + 3.184713376 Combine like terms: -3.184713376 + 3.184713376 = 0.000000000 0.000000000 + 1.197452229d + d2 = 0 + 3.184713376 1.197452229d + d2 = 0 + 3.184713376 Combine like terms: 0 + 3.184713376 = 3.184713376 1.197452229d + d2 = 3.184713376 The d term is 1.197452229d. Take half its coefficient (0.5987261145). Square it (0.3584729602) and add it to both sides. Add '0.3584729602' to each side of the equation. 1.197452229d + 0.3584729602 + d2 = 3.184713376 + 0.3584729602 Reorder the terms: 0.3584729602 + 1.197452229d + d2 = 3.184713376 + 0.3584729602 Combine like terms: 3.184713376 + 0.3584729602 = 3.5431863362 0.3584729602 + 1.197452229d + d2 = 3.5431863362 Factor a perfect square on the left side: (d + 0.5987261145)(d + 0.5987261145) = 3.5431863362 Calculate the square root of the right side: 1.882335341 Break this problem into two subproblems by setting (d + 0.5987261145) equal to 1.882335341 and -1.882335341.Subproblem 1
d + 0.5987261145 = 1.882335341 Simplifying d + 0.5987261145 = 1.882335341 Reorder the terms: 0.5987261145 + d = 1.882335341 Solving 0.5987261145 + d = 1.882335341 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.5987261145' to each side of the equation. 0.5987261145 + -0.5987261145 + d = 1.882335341 + -0.5987261145 Combine like terms: 0.5987261145 + -0.5987261145 = 0.0000000000 0.0000000000 + d = 1.882335341 + -0.5987261145 d = 1.882335341 + -0.5987261145 Combine like terms: 1.882335341 + -0.5987261145 = 1.2836092265 d = 1.2836092265 Simplifying d = 1.2836092265Subproblem 2
d + 0.5987261145 = -1.882335341 Simplifying d + 0.5987261145 = -1.882335341 Reorder the terms: 0.5987261145 + d = -1.882335341 Solving 0.5987261145 + d = -1.882335341 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.5987261145' to each side of the equation. 0.5987261145 + -0.5987261145 + d = -1.882335341 + -0.5987261145 Combine like terms: 0.5987261145 + -0.5987261145 = 0.0000000000 0.0000000000 + d = -1.882335341 + -0.5987261145 d = -1.882335341 + -0.5987261145 Combine like terms: -1.882335341 + -0.5987261145 = -2.4810614555 d = -2.4810614555 Simplifying d = -2.4810614555Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.2836092265, -2.4810614555}
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