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Simplifying (d + 4)(d + 4) = 5 Reorder the terms: (4 + d)(d + 4) = 5 Reorder the terms: (4 + d)(4 + d) = 5 Multiply (4 + d) * (4 + d) (4(4 + d) + d(4 + d)) = 5 ((4 * 4 + d * 4) + d(4 + d)) = 5 ((16 + 4d) + d(4 + d)) = 5 (16 + 4d + (4 * d + d * d)) = 5 (16 + 4d + (4d + d2)) = 5 Combine like terms: 4d + 4d = 8d (16 + 8d + d2) = 5 Solving 16 + 8d + d2 = 5 Solving for variable 'd'. Reorder the terms: 16 + -5 + 8d + d2 = 5 + -5 Combine like terms: 16 + -5 = 11 11 + 8d + d2 = 5 + -5 Combine like terms: 5 + -5 = 0 11 + 8d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 8d + -11 + d2 = 0 + -11 Reorder the terms: 11 + -11 + 8d + d2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 8d + d2 = 0 + -11 8d + d2 = 0 + -11 Combine like terms: 0 + -11 = -11 8d + d2 = -11 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 = -11 + 16 Reorder the terms: 16 + 8d + d2 = -11 + 16 Combine like terms: -11 + 16 = 5 16 + 8d + d2 = 5 Factor a perfect square on the left side: (d + 4)(d + 4) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (d + 4) equal to 2.236067978 and -2.236067978.Subproblem 1
d + 4 = 2.236067978 Simplifying d + 4 = 2.236067978 Reorder the terms: 4 + d = 2.236067978 Solving 4 + d = 2.236067978 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 = 2.236067978 + -4 Combine like terms: 4 + -4 = 0 0 + d = 2.236067978 + -4 d = 2.236067978 + -4 Combine like terms: 2.236067978 + -4 = -1.763932022 d = -1.763932022 Simplifying d = -1.763932022Subproblem 2
d + 4 = -2.236067978 Simplifying d + 4 = -2.236067978 Reorder the terms: 4 + d = -2.236067978 Solving 4 + d = -2.236067978 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 = -2.236067978 + -4 Combine like terms: 4 + -4 = 0 0 + d = -2.236067978 + -4 d = -2.236067978 + -4 Combine like terms: -2.236067978 + -4 = -6.236067978 d = -6.236067978 Simplifying d = -6.236067978Solution
The solution to the problem is based on the solutions from the subproblems. d = {-1.763932022, -6.236067978}
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