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Simplifying 16d2 + 4d + -3 = 0 Reorder the terms: -3 + 4d + 16d2 = 0 Solving -3 + 4d + 16d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.1875 + 0.25d + d2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + 0.25d + 0.1875 + d2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + 0.25d + d2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + 0.25d + d2 = 0 + 0.1875 0.25d + d2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 0.25d + d2 = 0.1875 The d term is 0.25d. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25d + 0.015625 + d2 = 0.1875 + 0.015625 Reorder the terms: 0.015625 + 0.25d + d2 = 0.1875 + 0.015625 Combine like terms: 0.1875 + 0.015625 = 0.203125 0.015625 + 0.25d + d2 = 0.203125 Factor a perfect square on the left side: (d + 0.125)(d + 0.125) = 0.203125 Calculate the square root of the right side: 0.450693909 Break this problem into two subproblems by setting (d + 0.125) equal to 0.450693909 and -0.450693909.Subproblem 1
d + 0.125 = 0.450693909 Simplifying d + 0.125 = 0.450693909 Reorder the terms: 0.125 + d = 0.450693909 Solving 0.125 + d = 0.450693909 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + d = 0.450693909 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + d = 0.450693909 + -0.125 d = 0.450693909 + -0.125 Combine like terms: 0.450693909 + -0.125 = 0.325693909 d = 0.325693909 Simplifying d = 0.325693909Subproblem 2
d + 0.125 = -0.450693909 Simplifying d + 0.125 = -0.450693909 Reorder the terms: 0.125 + d = -0.450693909 Solving 0.125 + d = -0.450693909 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + d = -0.450693909 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + d = -0.450693909 + -0.125 d = -0.450693909 + -0.125 Combine like terms: -0.450693909 + -0.125 = -0.575693909 d = -0.575693909 Simplifying d = -0.575693909Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.325693909, -0.575693909}
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