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Simplifying d(d + -2) = 46 Reorder the terms: d(-2 + d) = 46 (-2 * d + d * d) = 46 (-2d + d2) = 46 Solving -2d + d2 = 46 Solving for variable 'd'. Reorder the terms: -46 + -2d + d2 = 46 + -46 Combine like terms: 46 + -46 = 0 -46 + -2d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + -2d + 46 + d2 = 0 + 46 Reorder the terms: -46 + 46 + -2d + d2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + -2d + d2 = 0 + 46 -2d + d2 = 0 + 46 Combine like terms: 0 + 46 = 46 -2d + d2 = 46 The d term is -2d. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2d + 1 + d2 = 46 + 1 Reorder the terms: 1 + -2d + d2 = 46 + 1 Combine like terms: 46 + 1 = 47 1 + -2d + d2 = 47 Factor a perfect square on the left side: (d + -1)(d + -1) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (d + -1) equal to 6.8556546 and -6.8556546.Subproblem 1
d + -1 = 6.8556546 Simplifying d + -1 = 6.8556546 Reorder the terms: -1 + d = 6.8556546 Solving -1 + d = 6.8556546 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + d = 6.8556546 + 1 Combine like terms: -1 + 1 = 0 0 + d = 6.8556546 + 1 d = 6.8556546 + 1 Combine like terms: 6.8556546 + 1 = 7.8556546 d = 7.8556546 Simplifying d = 7.8556546Subproblem 2
d + -1 = -6.8556546 Simplifying d + -1 = -6.8556546 Reorder the terms: -1 + d = -6.8556546 Solving -1 + d = -6.8556546 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + d = -6.8556546 + 1 Combine like terms: -1 + 1 = 0 0 + d = -6.8556546 + 1 d = -6.8556546 + 1 Combine like terms: -6.8556546 + 1 = -5.8556546 d = -5.8556546 Simplifying d = -5.8556546Solution
The solution to the problem is based on the solutions from the subproblems. d = {7.8556546, -5.8556546}
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