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Simplifying -2d2 + -0.5d4 = -0.5 Solving -2d2 + -0.5d4 = -0.5 Solving for variable 'd'. Reorder the terms: 0.5 + -2d2 + -0.5d4 = -0.5 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.5 + -2d2 + -0.5d4 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -1 + 4d2 + d4 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 4d2 + 1 + d4 = 0 + 1 Reorder the terms: -1 + 1 + 4d2 + d4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4d2 + d4 = 0 + 1 4d2 + d4 = 0 + 1 Combine like terms: 0 + 1 = 1 4d2 + d4 = 1 The d term is 4d2. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4d2 + 4 + d4 = 1 + 4 Reorder the terms: 4 + 4d2 + d4 = 1 + 4 Combine like terms: 1 + 4 = 5 4 + 4d2 + d4 = 5 Factor a perfect square on the left side: (d2 + 2)(d2 + 2) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (d2 + 2) equal to 2.236067978 and -2.236067978.Subproblem 1
d2 + 2 = 2.236067978 Simplifying d2 + 2 = 2.236067978 Reorder the terms: 2 + d2 = 2.236067978 Solving 2 + d2 = 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 + d2 = 2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + d2 = 2.236067978 + -2 d2 = 2.236067978 + -2 Combine like terms: 2.236067978 + -2 = 0.236067978 d2 = 0.236067978 Simplifying d2 = 0.236067978 Take the square root of each side: d = {-0.485868272, 0.485868272}Subproblem 2
d2 + 2 = -2.236067978 Simplifying d2 + 2 = -2.236067978 Reorder the terms: 2 + d2 = -2.236067978 Solving 2 + d2 = -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 + d2 = -2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + d2 = -2.236067978 + -2 d2 = -2.236067978 + -2 Combine like terms: -2.236067978 + -2 = -4.236067978 d2 = -4.236067978 Simplifying d2 = -4.236067978 Reorder the terms: 4.236067978 + d2 = -4.236067978 + 4.236067978 Combine like terms: -4.236067978 + 4.236067978 = 0.000000000 4.236067978 + d2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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