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Simplifying 118.7d2 + 396.61d + 325.89 = 0 Reorder the terms: 325.89 + 396.61d + 118.7d2 = 0 Solving 325.89 + 396.61d + 118.7d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 118.7 the coefficient of the squared term: Divide each side by '118.7'. 2.745492839 + 3.341280539d + d2 = 0 Move the constant term to the right: Add '-2.745492839' to each side of the equation. 2.745492839 + 3.341280539d + -2.745492839 + d2 = 0 + -2.745492839 Reorder the terms: 2.745492839 + -2.745492839 + 3.341280539d + d2 = 0 + -2.745492839 Combine like terms: 2.745492839 + -2.745492839 = 0.000000000 0.000000000 + 3.341280539d + d2 = 0 + -2.745492839 3.341280539d + d2 = 0 + -2.745492839 Combine like terms: 0 + -2.745492839 = -2.745492839 3.341280539d + d2 = -2.745492839 The d term is 3.341280539d. Take half its coefficient (1.67064027). Square it (2.791038912) and add it to both sides. Add '2.791038912' to each side of the equation. 3.341280539d + 2.791038912 + d2 = -2.745492839 + 2.791038912 Reorder the terms: 2.791038912 + 3.341280539d + d2 = -2.745492839 + 2.791038912 Combine like terms: -2.745492839 + 2.791038912 = 0.045546073 2.791038912 + 3.341280539d + d2 = 0.045546073 Factor a perfect square on the left side: (d + 1.67064027)(d + 1.67064027) = 0.045546073 Calculate the square root of the right side: 0.21341526 Break this problem into two subproblems by setting (d + 1.67064027) equal to 0.21341526 and -0.21341526.Subproblem 1
d + 1.67064027 = 0.21341526 Simplifying d + 1.67064027 = 0.21341526 Reorder the terms: 1.67064027 + d = 0.21341526 Solving 1.67064027 + d = 0.21341526 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1.67064027' to each side of the equation. 1.67064027 + -1.67064027 + d = 0.21341526 + -1.67064027 Combine like terms: 1.67064027 + -1.67064027 = 0.00000000 0.00000000 + d = 0.21341526 + -1.67064027 d = 0.21341526 + -1.67064027 Combine like terms: 0.21341526 + -1.67064027 = -1.45722501 d = -1.45722501 Simplifying d = -1.45722501Subproblem 2
d + 1.67064027 = -0.21341526 Simplifying d + 1.67064027 = -0.21341526 Reorder the terms: 1.67064027 + d = -0.21341526 Solving 1.67064027 + d = -0.21341526 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1.67064027' to each side of the equation. 1.67064027 + -1.67064027 + d = -0.21341526 + -1.67064027 Combine like terms: 1.67064027 + -1.67064027 = 0.00000000 0.00000000 + d = -0.21341526 + -1.67064027 d = -0.21341526 + -1.67064027 Combine like terms: -0.21341526 + -1.67064027 = -1.88405553 d = -1.88405553 Simplifying d = -1.88405553Solution
The solution to the problem is based on the solutions from the subproblems. d = {-1.45722501, -1.88405553}
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