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Simplifying 2d2 + 7d + 3 = 2 Reorder the terms: 3 + 7d + 2d2 = 2 Solving 3 + 7d + 2d2 = 2 Solving for variable 'd'. Reorder the terms: 3 + -2 + 7d + 2d2 = 2 + -2 Combine like terms: 3 + -2 = 1 1 + 7d + 2d2 = 2 + -2 Combine like terms: 2 + -2 = 0 1 + 7d + 2d2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + 3.5d + d2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 3.5d + -0.5 + d2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 3.5d + d2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 3.5d + d2 = 0 + -0.5 3.5d + d2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 3.5d + d2 = -0.5 The d term is 3.5d. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5d + 3.0625 + d2 = -0.5 + 3.0625 Reorder the terms: 3.0625 + 3.5d + d2 = -0.5 + 3.0625 Combine like terms: -0.5 + 3.0625 = 2.5625 3.0625 + 3.5d + d2 = 2.5625 Factor a perfect square on the left side: (d + 1.75)(d + 1.75) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (d + 1.75) equal to 1.600781059 and -1.600781059.Subproblem 1
d + 1.75 = 1.600781059 Simplifying d + 1.75 = 1.600781059 Reorder the terms: 1.75 + d = 1.600781059 Solving 1.75 + d = 1.600781059 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + d = 1.600781059 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + d = 1.600781059 + -1.75 d = 1.600781059 + -1.75 Combine like terms: 1.600781059 + -1.75 = -0.149218941 d = -0.149218941 Simplifying d = -0.149218941Subproblem 2
d + 1.75 = -1.600781059 Simplifying d + 1.75 = -1.600781059 Reorder the terms: 1.75 + d = -1.600781059 Solving 1.75 + d = -1.600781059 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + d = -1.600781059 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + d = -1.600781059 + -1.75 d = -1.600781059 + -1.75 Combine like terms: -1.600781059 + -1.75 = -3.350781059 d = -3.350781059 Simplifying d = -3.350781059Solution
The solution to the problem is based on the solutions from the subproblems. d = {-0.149218941, -3.350781059}
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