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Simplifying 28d2 + 5d + -5 = 0 Reorder the terms: -5 + 5d + 28d2 = 0 Solving -5 + 5d + 28d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.1785714286 + 0.1785714286d + d2 = 0 Move the constant term to the right: Add '0.1785714286' to each side of the equation. -0.1785714286 + 0.1785714286d + 0.1785714286 + d2 = 0 + 0.1785714286 Reorder the terms: -0.1785714286 + 0.1785714286 + 0.1785714286d + d2 = 0 + 0.1785714286 Combine like terms: -0.1785714286 + 0.1785714286 = 0.0000000000 0.0000000000 + 0.1785714286d + d2 = 0 + 0.1785714286 0.1785714286d + d2 = 0 + 0.1785714286 Combine like terms: 0 + 0.1785714286 = 0.1785714286 0.1785714286d + d2 = 0.1785714286 The d term is 0.1785714286d. Take half its coefficient (0.0892857143). Square it (0.007971938778) and add it to both sides. Add '0.007971938778' to each side of the equation. 0.1785714286d + 0.007971938778 + d2 = 0.1785714286 + 0.007971938778 Reorder the terms: 0.007971938778 + 0.1785714286d + d2 = 0.1785714286 + 0.007971938778 Combine like terms: 0.1785714286 + 0.007971938778 = 0.186543367378 0.007971938778 + 0.1785714286d + d2 = 0.186543367378 Factor a perfect square on the left side: (d + 0.0892857143)(d + 0.0892857143) = 0.186543367378 Calculate the square root of the right side: 0.431906665 Break this problem into two subproblems by setting (d + 0.0892857143) equal to 0.431906665 and -0.431906665.Subproblem 1
d + 0.0892857143 = 0.431906665 Simplifying d + 0.0892857143 = 0.431906665 Reorder the terms: 0.0892857143 + d = 0.431906665 Solving 0.0892857143 + d = 0.431906665 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.0892857143' to each side of the equation. 0.0892857143 + -0.0892857143 + d = 0.431906665 + -0.0892857143 Combine like terms: 0.0892857143 + -0.0892857143 = 0.0000000000 0.0000000000 + d = 0.431906665 + -0.0892857143 d = 0.431906665 + -0.0892857143 Combine like terms: 0.431906665 + -0.0892857143 = 0.3426209507 d = 0.3426209507 Simplifying d = 0.3426209507Subproblem 2
d + 0.0892857143 = -0.431906665 Simplifying d + 0.0892857143 = -0.431906665 Reorder the terms: 0.0892857143 + d = -0.431906665 Solving 0.0892857143 + d = -0.431906665 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.0892857143' to each side of the equation. 0.0892857143 + -0.0892857143 + d = -0.431906665 + -0.0892857143 Combine like terms: 0.0892857143 + -0.0892857143 = 0.0000000000 0.0000000000 + d = -0.431906665 + -0.0892857143 d = -0.431906665 + -0.0892857143 Combine like terms: -0.431906665 + -0.0892857143 = -0.5211923793 d = -0.5211923793 Simplifying d = -0.5211923793Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.3426209507, -0.5211923793}
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