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Simplifying 0.2d(d + -6) = 0.3d + 5 + -3 + 0.1d Reorder the terms: 0.2d(-6 + d) = 0.3d + 5 + -3 + 0.1d (-6 * 0.2d + d * 0.2d) = 0.3d + 5 + -3 + 0.1d (-1.2d + 0.2d2) = 0.3d + 5 + -3 + 0.1d Reorder the terms: -1.2d + 0.2d2 = 5 + -3 + 0.3d + 0.1d Combine like terms: 5 + -3 = 2 -1.2d + 0.2d2 = 2 + 0.3d + 0.1d Combine like terms: 0.3d + 0.1d = 0.4d -1.2d + 0.2d2 = 2 + 0.4d Solving -1.2d + 0.2d2 = 2 + 0.4d Solving for variable 'd'. Reorder the terms: -2 + -1.2d + -0.4d + 0.2d2 = 2 + 0.4d + -2 + -0.4d Combine like terms: -1.2d + -0.4d = -1.6d -2 + -1.6d + 0.2d2 = 2 + 0.4d + -2 + -0.4d Reorder the terms: -2 + -1.6d + 0.2d2 = 2 + -2 + 0.4d + -0.4d Combine like terms: 2 + -2 = 0 -2 + -1.6d + 0.2d2 = 0 + 0.4d + -0.4d -2 + -1.6d + 0.2d2 = 0.4d + -0.4d Combine like terms: 0.4d + -0.4d = 0.0 -2 + -1.6d + 0.2d2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -10 + -8d + d2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -8d + 10 + d2 = 0 + 10 Reorder the terms: -10 + 10 + -8d + d2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -8d + d2 = 0 + 10 -8d + d2 = 0 + 10 Combine like terms: 0 + 10 = 10 -8d + d2 = 10 The d term is -8d. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8d + 16 + d2 = 10 + 16 Reorder the terms: 16 + -8d + d2 = 10 + 16 Combine like terms: 10 + 16 = 26 16 + -8d + d2 = 26 Factor a perfect square on the left side: (d + -4)(d + -4) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (d + -4) equal to 5.099019514 and -5.099019514.Subproblem 1
d + -4 = 5.099019514 Simplifying d + -4 = 5.099019514 Reorder the terms: -4 + d = 5.099019514 Solving -4 + d = 5.099019514 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + d = 5.099019514 + 4 Combine like terms: -4 + 4 = 0 0 + d = 5.099019514 + 4 d = 5.099019514 + 4 Combine like terms: 5.099019514 + 4 = 9.099019514 d = 9.099019514 Simplifying d = 9.099019514Subproblem 2
d + -4 = -5.099019514 Simplifying d + -4 = -5.099019514 Reorder the terms: -4 + d = -5.099019514 Solving -4 + d = -5.099019514 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + d = -5.099019514 + 4 Combine like terms: -4 + 4 = 0 0 + d = -5.099019514 + 4 d = -5.099019514 + 4 Combine like terms: -5.099019514 + 4 = -1.099019514 d = -1.099019514 Simplifying d = -1.099019514Solution
The solution to the problem is based on the solutions from the subproblems. d = {9.099019514, -1.099019514}
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