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Simplifying 2d2 + 4d + -13 = 0 Reorder the terms: -13 + 4d + 2d2 = 0 Solving -13 + 4d + 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'. -6.5 + 2d + d2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + 2d + 6.5 + d2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + 2d + d2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + 2d + d2 = 0 + 6.5 2d + d2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 2d + d2 = 6.5 The d term is 2d. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2d + 1 + d2 = 6.5 + 1 Reorder the terms: 1 + 2d + d2 = 6.5 + 1 Combine like terms: 6.5 + 1 = 7.5 1 + 2d + d2 = 7.5 Factor a perfect square on the left side: (d + 1)(d + 1) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (d + 1) equal to 2.738612788 and -2.738612788.Subproblem 1
d + 1 = 2.738612788 Simplifying d + 1 = 2.738612788 Reorder the terms: 1 + d = 2.738612788 Solving 1 + d = 2.738612788 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + d = 2.738612788 + -1 Combine like terms: 1 + -1 = 0 0 + d = 2.738612788 + -1 d = 2.738612788 + -1 Combine like terms: 2.738612788 + -1 = 1.738612788 d = 1.738612788 Simplifying d = 1.738612788Subproblem 2
d + 1 = -2.738612788 Simplifying d + 1 = -2.738612788 Reorder the terms: 1 + d = -2.738612788 Solving 1 + d = -2.738612788 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + d = -2.738612788 + -1 Combine like terms: 1 + -1 = 0 0 + d = -2.738612788 + -1 d = -2.738612788 + -1 Combine like terms: -2.738612788 + -1 = -3.738612788 d = -3.738612788 Simplifying d = -3.738612788Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.738612788, -3.738612788}
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