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Simplifying (d + 3d) + -1(-1d + 2) * d = 5 Combine like terms: d + 3d = 4d (4d) + -1(-1d + 2) * d = 5 (4d) + -1(-1d + 2) * d = 5 Reorder the terms: (4d) + -1(2 + -1d) * d = 5 Reorder the terms for easier multiplication: (4d) + -1d(2 + -1d) = 5 (4d) + (2 * -1d + -1d * -1d) = 5 (4d) + (-2d + 1d2) = 5 Combine like terms: (4d) + -2d = 2d 2d + 1d2 = 5 Solving 2d + 1d2 = 5 Solving for variable 'd'. Reorder the terms: -5 + 2d + 1d2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 2d + 1d2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 2d + 5 + d2 = 0 + 5 Reorder the terms: -5 + 5 + 2d + d2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2d + d2 = 0 + 5 2d + d2 = 0 + 5 Combine like terms: 0 + 5 = 5 2d + d2 = 5 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 = 5 + 1 Reorder the terms: 1 + 2d + d2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + 2d + d2 = 6 Factor a perfect square on the left side: (d + 1)(d + 1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (d + 1) equal to 2.449489743 and -2.449489743.Subproblem 1
d + 1 = 2.449489743 Simplifying d + 1 = 2.449489743 Reorder the terms: 1 + d = 2.449489743 Solving 1 + d = 2.449489743 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 = 2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + d = 2.449489743 + -1 d = 2.449489743 + -1 Combine like terms: 2.449489743 + -1 = 1.449489743 d = 1.449489743 Simplifying d = 1.449489743Subproblem 2
d + 1 = -2.449489743 Simplifying d + 1 = -2.449489743 Reorder the terms: 1 + d = -2.449489743 Solving 1 + d = -2.449489743 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 = -2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + d = -2.449489743 + -1 d = -2.449489743 + -1 Combine like terms: -2.449489743 + -1 = -3.449489743 d = -3.449489743 Simplifying d = -3.449489743Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.449489743, -3.449489743}
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