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Simplifying (d2 + -3d) + (d + -4) = 0 Reorder the terms: (-3d + d2) + (d + -4) = 0 Remove parenthesis around (-3d + d2) -3d + d2 + (d + -4) = 0 Reorder the terms: -3d + d2 + (-4 + d) = 0 Remove parenthesis around (-4 + d) -3d + d2 + -4 + d = 0 Reorder the terms: -4 + -3d + d + d2 = 0 Combine like terms: -3d + d = -2d -4 + -2d + d2 = 0 Solving -4 + -2d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -2d + 4 + d2 = 0 + 4 Reorder the terms: -4 + 4 + -2d + d2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2d + d2 = 0 + 4 -2d + d2 = 0 + 4 Combine like terms: 0 + 4 = 4 -2d + d2 = 4 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 = 4 + 1 Reorder the terms: 1 + -2d + d2 = 4 + 1 Combine like terms: 4 + 1 = 5 1 + -2d + d2 = 5 Factor a perfect square on the left side: (d + -1)(d + -1) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (d + -1) equal to 2.236067978 and -2.236067978.Subproblem 1
d + -1 = 2.236067978 Simplifying d + -1 = 2.236067978 Reorder the terms: -1 + d = 2.236067978 Solving -1 + d = 2.236067978 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 = 2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + d = 2.236067978 + 1 d = 2.236067978 + 1 Combine like terms: 2.236067978 + 1 = 3.236067978 d = 3.236067978 Simplifying d = 3.236067978Subproblem 2
d + -1 = -2.236067978 Simplifying d + -1 = -2.236067978 Reorder the terms: -1 + d = -2.236067978 Solving -1 + d = -2.236067978 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 = -2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + d = -2.236067978 + 1 d = -2.236067978 + 1 Combine like terms: -2.236067978 + 1 = -1.236067978 d = -1.236067978 Simplifying d = -1.236067978Solution
The solution to the problem is based on the solutions from the subproblems. d = {3.236067978, -1.236067978}
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