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Simplifying -0.05d2 + 16.9d = 34 Reorder the terms: 16.9d + -0.05d2 = 34 Solving 16.9d + -0.05d2 = 34 Solving for variable 'd'. Reorder the terms: -34 + 16.9d + -0.05d2 = 34 + -34 Combine like terms: 34 + -34 = 0 -34 + 16.9d + -0.05d2 = 0 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. 680 + -338d + d2 = 0 Move the constant term to the right: Add '-680' to each side of the equation. 680 + -338d + -680 + d2 = 0 + -680 Reorder the terms: 680 + -680 + -338d + d2 = 0 + -680 Combine like terms: 680 + -680 = 0 0 + -338d + d2 = 0 + -680 -338d + d2 = 0 + -680 Combine like terms: 0 + -680 = -680 -338d + d2 = -680 The d term is -338d. Take half its coefficient (-169). Square it (28561) and add it to both sides. Add '28561' to each side of the equation. -338d + 28561 + d2 = -680 + 28561 Reorder the terms: 28561 + -338d + d2 = -680 + 28561 Combine like terms: -680 + 28561 = 27881 28561 + -338d + d2 = 27881 Factor a perfect square on the left side: (d + -169)(d + -169) = 27881 Calculate the square root of the right side: 166.976046186 Break this problem into two subproblems by setting (d + -169) equal to 166.976046186 and -166.976046186.Subproblem 1
d + -169 = 166.976046186 Simplifying d + -169 = 166.976046186 Reorder the terms: -169 + d = 166.976046186 Solving -169 + d = 166.976046186 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '169' to each side of the equation. -169 + 169 + d = 166.976046186 + 169 Combine like terms: -169 + 169 = 0 0 + d = 166.976046186 + 169 d = 166.976046186 + 169 Combine like terms: 166.976046186 + 169 = 335.976046186 d = 335.976046186 Simplifying d = 335.976046186Subproblem 2
d + -169 = -166.976046186 Simplifying d + -169 = -166.976046186 Reorder the terms: -169 + d = -166.976046186 Solving -169 + d = -166.976046186 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '169' to each side of the equation. -169 + 169 + d = -166.976046186 + 169 Combine like terms: -169 + 169 = 0 0 + d = -166.976046186 + 169 d = -166.976046186 + 169 Combine like terms: -166.976046186 + 169 = 2.023953814 d = 2.023953814 Simplifying d = 2.023953814Solution
The solution to the problem is based on the solutions from the subproblems. d = {335.976046186, 2.023953814}
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