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Simplifying (d + 7)(d + 1) = 5 Reorder the terms: (7 + d)(d + 1) = 5 Reorder the terms: (7 + d)(1 + d) = 5 Multiply (7 + d) * (1 + d) (7(1 + d) + d(1 + d)) = 5 ((1 * 7 + d * 7) + d(1 + d)) = 5 ((7 + 7d) + d(1 + d)) = 5 (7 + 7d + (1 * d + d * d)) = 5 (7 + 7d + (1d + d2)) = 5 Combine like terms: 7d + 1d = 8d (7 + 8d + d2) = 5 Solving 7 + 8d + d2 = 5 Solving for variable 'd'. Reorder the terms: 7 + -5 + 8d + d2 = 5 + -5 Combine like terms: 7 + -5 = 2 2 + 8d + d2 = 5 + -5 Combine like terms: 5 + -5 = 0 2 + 8d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 8d + -2 + d2 = 0 + -2 Reorder the terms: 2 + -2 + 8d + d2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 8d + d2 = 0 + -2 8d + d2 = 0 + -2 Combine like terms: 0 + -2 = -2 8d + d2 = -2 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 = -2 + 16 Reorder the terms: 16 + 8d + d2 = -2 + 16 Combine like terms: -2 + 16 = 14 16 + 8d + d2 = 14 Factor a perfect square on the left side: (d + 4)(d + 4) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (d + 4) equal to 3.741657387 and -3.741657387.Subproblem 1
d + 4 = 3.741657387 Simplifying d + 4 = 3.741657387 Reorder the terms: 4 + d = 3.741657387 Solving 4 + d = 3.741657387 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 = 3.741657387 + -4 Combine like terms: 4 + -4 = 0 0 + d = 3.741657387 + -4 d = 3.741657387 + -4 Combine like terms: 3.741657387 + -4 = -0.258342613 d = -0.258342613 Simplifying d = -0.258342613Subproblem 2
d + 4 = -3.741657387 Simplifying d + 4 = -3.741657387 Reorder the terms: 4 + d = -3.741657387 Solving 4 + d = -3.741657387 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 = -3.741657387 + -4 Combine like terms: 4 + -4 = 0 0 + d = -3.741657387 + -4 d = -3.741657387 + -4 Combine like terms: -3.741657387 + -4 = -7.741657387 d = -7.741657387 Simplifying d = -7.741657387Solution
The solution to the problem is based on the solutions from the subproblems. d = {-0.258342613, -7.741657387}
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