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Simplifying 2d2 + 13d + -6 = 0 Reorder the terms: -6 + 13d + 2d2 = 0 Solving -6 + 13d + 2d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + 6.5d + d2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 6.5d + 3 + d2 = 0 + 3 Reorder the terms: -3 + 3 + 6.5d + d2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 6.5d + d2 = 0 + 3 6.5d + d2 = 0 + 3 Combine like terms: 0 + 3 = 3 6.5d + d2 = 3 The d term is 6.5d. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5d + 10.5625 + d2 = 3 + 10.5625 Reorder the terms: 10.5625 + 6.5d + d2 = 3 + 10.5625 Combine like terms: 3 + 10.5625 = 13.5625 10.5625 + 6.5d + d2 = 13.5625 Factor a perfect square on the left side: (d + 3.25)(d + 3.25) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (d + 3.25) equal to 3.682729966 and -3.682729966.Subproblem 1
d + 3.25 = 3.682729966 Simplifying d + 3.25 = 3.682729966 Reorder the terms: 3.25 + d = 3.682729966 Solving 3.25 + d = 3.682729966 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + d = 3.682729966 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + d = 3.682729966 + -3.25 d = 3.682729966 + -3.25 Combine like terms: 3.682729966 + -3.25 = 0.432729966 d = 0.432729966 Simplifying d = 0.432729966Subproblem 2
d + 3.25 = -3.682729966 Simplifying d + 3.25 = -3.682729966 Reorder the terms: 3.25 + d = -3.682729966 Solving 3.25 + d = -3.682729966 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + d = -3.682729966 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + d = -3.682729966 + -3.25 d = -3.682729966 + -3.25 Combine like terms: -3.682729966 + -3.25 = -6.932729966 d = -6.932729966 Simplifying d = -6.932729966Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.432729966, -6.932729966}
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