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Simplifying 4D2 + 8D + -10 = 0 Reorder the terms: -10 + 8D + 4D2 = 0 Solving -10 + 8D + 4D2 = 0 Solving for variable 'D'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 4D + 2D2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 4D + 2D2)' equal to zero and attempt to solve: Simplifying -5 + 4D + 2D2 = 0 Solving -5 + 4D + 2D2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + 2D + D2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 2D + 2.5 + D2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 2D + D2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 2D + D2 = 0 + 2.5 2D + D2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 2D + D2 = 2.5 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 = 2.5 + 1 Reorder the terms: 1 + 2D + D2 = 2.5 + 1 Combine like terms: 2.5 + 1 = 3.5 1 + 2D + D2 = 3.5 Factor a perfect square on the left side: (D + 1)(D + 1) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (D + 1) equal to 1.870828693 and -1.870828693.Subproblem 1
D + 1 = 1.870828693 Simplifying D + 1 = 1.870828693 Reorder the terms: 1 + D = 1.870828693 Solving 1 + D = 1.870828693 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 = 1.870828693 + -1 Combine like terms: 1 + -1 = 0 0 + D = 1.870828693 + -1 D = 1.870828693 + -1 Combine like terms: 1.870828693 + -1 = 0.870828693 D = 0.870828693 Simplifying D = 0.870828693Subproblem 2
D + 1 = -1.870828693 Simplifying D + 1 = -1.870828693 Reorder the terms: 1 + D = -1.870828693 Solving 1 + D = -1.870828693 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 = -1.870828693 + -1 Combine like terms: 1 + -1 = 0 0 + D = -1.870828693 + -1 D = -1.870828693 + -1 Combine like terms: -1.870828693 + -1 = -2.870828693 D = -2.870828693 Simplifying D = -2.870828693Solution
The solution to the problem is based on the solutions from the subproblems. D = {0.870828693, -2.870828693}Solution
D = {0.870828693, -2.870828693}
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