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Simplifying 592 = 4.25d + 6.8d2 Solving 592 = 4.25d + 6.8d2 Solving for variable 'd'. Reorder the terms: 592 + -4.25d + -6.8d2 = 4.25d + -4.25d + 6.8d2 + -6.8d2 Combine like terms: 4.25d + -4.25d = 0.00 592 + -4.25d + -6.8d2 = 0.00 + 6.8d2 + -6.8d2 592 + -4.25d + -6.8d2 = 6.8d2 + -6.8d2 Combine like terms: 6.8d2 + -6.8d2 = 0.0 592 + -4.25d + -6.8d2 = 0.0 Begin completing the square. Divide all terms by -6.8 the coefficient of the squared term: Divide each side by '-6.8'. -87.05882353 + 0.625d + d2 = 0 Move the constant term to the right: Add '87.05882353' to each side of the equation. -87.05882353 + 0.625d + 87.05882353 + d2 = 0 + 87.05882353 Reorder the terms: -87.05882353 + 87.05882353 + 0.625d + d2 = 0 + 87.05882353 Combine like terms: -87.05882353 + 87.05882353 = 0.00000000 0.00000000 + 0.625d + d2 = 0 + 87.05882353 0.625d + d2 = 0 + 87.05882353 Combine like terms: 0 + 87.05882353 = 87.05882353 0.625d + d2 = 87.05882353 The d term is 0.625d. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625d + 0.09765625 + d2 = 87.05882353 + 0.09765625 Reorder the terms: 0.09765625 + 0.625d + d2 = 87.05882353 + 0.09765625 Combine like terms: 87.05882353 + 0.09765625 = 87.15647978 0.09765625 + 0.625d + d2 = 87.15647978 Factor a perfect square on the left side: (d + 0.3125)(d + 0.3125) = 87.15647978 Calculate the square root of the right side: 9.335763481 Break this problem into two subproblems by setting (d + 0.3125) equal to 9.335763481 and -9.335763481.Subproblem 1
d + 0.3125 = 9.335763481 Simplifying d + 0.3125 = 9.335763481 Reorder the terms: 0.3125 + d = 9.335763481 Solving 0.3125 + d = 9.335763481 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + d = 9.335763481 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + d = 9.335763481 + -0.3125 d = 9.335763481 + -0.3125 Combine like terms: 9.335763481 + -0.3125 = 9.023263481 d = 9.023263481 Simplifying d = 9.023263481Subproblem 2
d + 0.3125 = -9.335763481 Simplifying d + 0.3125 = -9.335763481 Reorder the terms: 0.3125 + d = -9.335763481 Solving 0.3125 + d = -9.335763481 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + d = -9.335763481 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + d = -9.335763481 + -0.3125 d = -9.335763481 + -0.3125 Combine like terms: -9.335763481 + -0.3125 = -9.648263481 d = -9.648263481 Simplifying d = -9.648263481Solution
The solution to the problem is based on the solutions from the subproblems. d = {9.023263481, -9.648263481}
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