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Simplifying d2 + 13d + -1638 = 0 Reorder the terms: -1638 + 13d + d2 = 0 Solving -1638 + 13d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '1638' to each side of the equation. -1638 + 13d + 1638 + d2 = 0 + 1638 Reorder the terms: -1638 + 1638 + 13d + d2 = 0 + 1638 Combine like terms: -1638 + 1638 = 0 0 + 13d + d2 = 0 + 1638 13d + d2 = 0 + 1638 Combine like terms: 0 + 1638 = 1638 13d + d2 = 1638 The d term is 13d. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13d + 42.25 + d2 = 1638 + 42.25 Reorder the terms: 42.25 + 13d + d2 = 1638 + 42.25 Combine like terms: 1638 + 42.25 = 1680.25 42.25 + 13d + d2 = 1680.25 Factor a perfect square on the left side: (d + 6.5)(d + 6.5) = 1680.25 Calculate the square root of the right side: 40.990852638 Break this problem into two subproblems by setting (d + 6.5) equal to 40.990852638 and -40.990852638.Subproblem 1
d + 6.5 = 40.990852638 Simplifying d + 6.5 = 40.990852638 Reorder the terms: 6.5 + d = 40.990852638 Solving 6.5 + d = 40.990852638 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + d = 40.990852638 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + d = 40.990852638 + -6.5 d = 40.990852638 + -6.5 Combine like terms: 40.990852638 + -6.5 = 34.490852638 d = 34.490852638 Simplifying d = 34.490852638Subproblem 2
d + 6.5 = -40.990852638 Simplifying d + 6.5 = -40.990852638 Reorder the terms: 6.5 + d = -40.990852638 Solving 6.5 + d = -40.990852638 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + d = -40.990852638 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + d = -40.990852638 + -6.5 d = -40.990852638 + -6.5 Combine like terms: -40.990852638 + -6.5 = -47.490852638 d = -47.490852638 Simplifying d = -47.490852638Solution
The solution to the problem is based on the solutions from the subproblems. d = {34.490852638, -47.490852638}
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