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Simplifying 3d2 + 6d + -8 = 0 Reorder the terms: -8 + 6d + 3d2 = 0 Solving -8 + 6d + 3d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.666666667 + 2d + d2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 2d + 2.666666667 + d2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 2d + d2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 2d + d2 = 0 + 2.666666667 2d + d2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 2d + d2 = 2.666666667 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 = 2.666666667 + 1 Reorder the terms: 1 + 2d + d2 = 2.666666667 + 1 Combine like terms: 2.666666667 + 1 = 3.666666667 1 + 2d + d2 = 3.666666667 Factor a perfect square on the left side: (d + 1)(d + 1) = 3.666666667 Calculate the square root of the right side: 1.914854216 Break this problem into two subproblems by setting (d + 1) equal to 1.914854216 and -1.914854216.Subproblem 1
d + 1 = 1.914854216 Simplifying d + 1 = 1.914854216 Reorder the terms: 1 + d = 1.914854216 Solving 1 + d = 1.914854216 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 = 1.914854216 + -1 Combine like terms: 1 + -1 = 0 0 + d = 1.914854216 + -1 d = 1.914854216 + -1 Combine like terms: 1.914854216 + -1 = 0.914854216 d = 0.914854216 Simplifying d = 0.914854216Subproblem 2
d + 1 = -1.914854216 Simplifying d + 1 = -1.914854216 Reorder the terms: 1 + d = -1.914854216 Solving 1 + d = -1.914854216 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 = -1.914854216 + -1 Combine like terms: 1 + -1 = 0 0 + d = -1.914854216 + -1 d = -1.914854216 + -1 Combine like terms: -1.914854216 + -1 = -2.914854216 d = -2.914854216 Simplifying d = -2.914854216Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.914854216, -2.914854216}
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