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Simplifying 5 + 26d = -8d2 Solving 5 + 26d = -8d2 Solving for variable 'd'. Combine like terms: -8d2 + 8d2 = 0 5 + 26d + 8d2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + 3.25d + d2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + 3.25d + -0.625 + d2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + 3.25d + d2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + 3.25d + d2 = 0 + -0.625 3.25d + d2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 3.25d + d2 = -0.625 The d term is 3.25d. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25d + 2.640625 + d2 = -0.625 + 2.640625 Reorder the terms: 2.640625 + 3.25d + d2 = -0.625 + 2.640625 Combine like terms: -0.625 + 2.640625 = 2.015625 2.640625 + 3.25d + d2 = 2.015625 Factor a perfect square on the left side: (d + 1.625)(d + 1.625) = 2.015625 Calculate the square root of the right side: 1.419727086 Break this problem into two subproblems by setting (d + 1.625) equal to 1.419727086 and -1.419727086.Subproblem 1
d + 1.625 = 1.419727086 Simplifying d + 1.625 = 1.419727086 Reorder the terms: 1.625 + d = 1.419727086 Solving 1.625 + d = 1.419727086 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + d = 1.419727086 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + d = 1.419727086 + -1.625 d = 1.419727086 + -1.625 Combine like terms: 1.419727086 + -1.625 = -0.205272914 d = -0.205272914 Simplifying d = -0.205272914Subproblem 2
d + 1.625 = -1.419727086 Simplifying d + 1.625 = -1.419727086 Reorder the terms: 1.625 + d = -1.419727086 Solving 1.625 + d = -1.419727086 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + d = -1.419727086 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + d = -1.419727086 + -1.625 d = -1.419727086 + -1.625 Combine like terms: -1.419727086 + -1.625 = -3.044727086 d = -3.044727086 Simplifying d = -3.044727086Solution
The solution to the problem is based on the solutions from the subproblems. d = {-0.205272914, -3.044727086}
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