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Simplifying 5d2 + -43d + 6 = 0 Reorder the terms: 6 + -43d + 5d2 = 0 Solving 6 + -43d + 5d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.2 + -8.6d + d2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + -8.6d + -1.2 + d2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + -8.6d + d2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + -8.6d + d2 = 0 + -1.2 -8.6d + d2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 -8.6d + d2 = -1.2 The d term is -8.6d. Take half its coefficient (-4.3). Square it (18.49) and add it to both sides. Add '18.49' to each side of the equation. -8.6d + 18.49 + d2 = -1.2 + 18.49 Reorder the terms: 18.49 + -8.6d + d2 = -1.2 + 18.49 Combine like terms: -1.2 + 18.49 = 17.29 18.49 + -8.6d + d2 = 17.29 Factor a perfect square on the left side: (d + -4.3)(d + -4.3) = 17.29 Calculate the square root of the right side: 4.158124577 Break this problem into two subproblems by setting (d + -4.3) equal to 4.158124577 and -4.158124577.Subproblem 1
d + -4.3 = 4.158124577 Simplifying d + -4.3 = 4.158124577 Reorder the terms: -4.3 + d = 4.158124577 Solving -4.3 + d = 4.158124577 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4.3' to each side of the equation. -4.3 + 4.3 + d = 4.158124577 + 4.3 Combine like terms: -4.3 + 4.3 = 0.0 0.0 + d = 4.158124577 + 4.3 d = 4.158124577 + 4.3 Combine like terms: 4.158124577 + 4.3 = 8.458124577 d = 8.458124577 Simplifying d = 8.458124577Subproblem 2
d + -4.3 = -4.158124577 Simplifying d + -4.3 = -4.158124577 Reorder the terms: -4.3 + d = -4.158124577 Solving -4.3 + d = -4.158124577 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4.3' to each side of the equation. -4.3 + 4.3 + d = -4.158124577 + 4.3 Combine like terms: -4.3 + 4.3 = 0.0 0.0 + d = -4.158124577 + 4.3 d = -4.158124577 + 4.3 Combine like terms: -4.158124577 + 4.3 = 0.141875423 d = 0.141875423 Simplifying d = 0.141875423Solution
The solution to the problem is based on the solutions from the subproblems. d = {8.458124577, 0.141875423}
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