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Simplifying 118.7d2 + 397.61d + 325.89 = 0 Reorder the terms: 325.89 + 397.61d + 118.7d2 = 0 Solving 325.89 + 397.61d + 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 + 3.349705139d + d2 = 0 Move the constant term to the right: Add '-2.745492839' to each side of the equation. 2.745492839 + 3.349705139d + -2.745492839 + d2 = 0 + -2.745492839 Reorder the terms: 2.745492839 + -2.745492839 + 3.349705139d + d2 = 0 + -2.745492839 Combine like terms: 2.745492839 + -2.745492839 = 0.000000000 0.000000000 + 3.349705139d + d2 = 0 + -2.745492839 3.349705139d + d2 = 0 + -2.745492839 Combine like terms: 0 + -2.745492839 = -2.745492839 3.349705139d + d2 = -2.745492839 The d term is 3.349705139d. Take half its coefficient (1.67485257). Square it (2.805131131) and add it to both sides. Add '2.805131131' to each side of the equation. 3.349705139d + 2.805131131 + d2 = -2.745492839 + 2.805131131 Reorder the terms: 2.805131131 + 3.349705139d + d2 = -2.745492839 + 2.805131131 Combine like terms: -2.745492839 + 2.805131131 = 0.059638292 2.805131131 + 3.349705139d + d2 = 0.059638292 Factor a perfect square on the left side: (d + 1.67485257)(d + 1.67485257) = 0.059638292 Calculate the square root of the right side: 0.244209525 Break this problem into two subproblems by setting (d + 1.67485257) equal to 0.244209525 and -0.244209525.Subproblem 1
d + 1.67485257 = 0.244209525 Simplifying d + 1.67485257 = 0.244209525 Reorder the terms: 1.67485257 + d = 0.244209525 Solving 1.67485257 + d = 0.244209525 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1.67485257' to each side of the equation. 1.67485257 + -1.67485257 + d = 0.244209525 + -1.67485257 Combine like terms: 1.67485257 + -1.67485257 = 0.00000000 0.00000000 + d = 0.244209525 + -1.67485257 d = 0.244209525 + -1.67485257 Combine like terms: 0.244209525 + -1.67485257 = -1.430643045 d = -1.430643045 Simplifying d = -1.430643045Subproblem 2
d + 1.67485257 = -0.244209525 Simplifying d + 1.67485257 = -0.244209525 Reorder the terms: 1.67485257 + d = -0.244209525 Solving 1.67485257 + d = -0.244209525 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1.67485257' to each side of the equation. 1.67485257 + -1.67485257 + d = -0.244209525 + -1.67485257 Combine like terms: 1.67485257 + -1.67485257 = 0.00000000 0.00000000 + d = -0.244209525 + -1.67485257 d = -0.244209525 + -1.67485257 Combine like terms: -0.244209525 + -1.67485257 = -1.919062095 d = -1.919062095 Simplifying d = -1.919062095Solution
The solution to the problem is based on the solutions from the subproblems. d = {-1.430643045, -1.919062095}
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