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Simplifying (d + -3)(d + -1) = 4 Reorder the terms: (-3 + d)(d + -1) = 4 Reorder the terms: (-3 + d)(-1 + d) = 4 Multiply (-3 + d) * (-1 + d) (-3(-1 + d) + d(-1 + d)) = 4 ((-1 * -3 + d * -3) + d(-1 + d)) = 4 ((3 + -3d) + d(-1 + d)) = 4 (3 + -3d + (-1 * d + d * d)) = 4 (3 + -3d + (-1d + d2)) = 4 Combine like terms: -3d + -1d = -4d (3 + -4d + d2) = 4 Solving 3 + -4d + d2 = 4 Solving for variable 'd'. Reorder the terms: 3 + -4 + -4d + d2 = 4 + -4 Combine like terms: 3 + -4 = -1 -1 + -4d + d2 = 4 + -4 Combine like terms: 4 + -4 = 0 -1 + -4d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -4d + 1 + d2 = 0 + 1 Reorder the terms: -1 + 1 + -4d + d2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4d + d2 = 0 + 1 -4d + d2 = 0 + 1 Combine like terms: 0 + 1 = 1 -4d + d2 = 1 The d term is -4d. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4d + 4 + d2 = 1 + 4 Reorder the terms: 4 + -4d + d2 = 1 + 4 Combine like terms: 1 + 4 = 5 4 + -4d + d2 = 5 Factor a perfect square on the left side: (d + -2)(d + -2) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (d + -2) equal to 2.236067978 and -2.236067978.Subproblem 1
d + -2 = 2.236067978 Simplifying d + -2 = 2.236067978 Reorder the terms: -2 + d = 2.236067978 Solving -2 + d = 2.236067978 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + d = 2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + d = 2.236067978 + 2 d = 2.236067978 + 2 Combine like terms: 2.236067978 + 2 = 4.236067978 d = 4.236067978 Simplifying d = 4.236067978Subproblem 2
d + -2 = -2.236067978 Simplifying d + -2 = -2.236067978 Reorder the terms: -2 + d = -2.236067978 Solving -2 + d = -2.236067978 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + d = -2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + d = -2.236067978 + 2 d = -2.236067978 + 2 Combine like terms: -2.236067978 + 2 = -0.236067978 d = -0.236067978 Simplifying d = -0.236067978Solution
The solution to the problem is based on the solutions from the subproblems. d = {4.236067978, -0.236067978}
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