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Simplifying w2 + -2w = 4 Reorder the terms: -2w + w2 = 4 Solving -2w + w2 = 4 Solving for variable 'w'. Reorder the terms: -4 + -2w + w2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -2w + 4 + w2 = 0 + 4 Reorder the terms: -4 + 4 + -2w + w2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2w + w2 = 0 + 4 -2w + w2 = 0 + 4 Combine like terms: 0 + 4 = 4 -2w + w2 = 4 The w term is -2w. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2w + 1 + w2 = 4 + 1 Reorder the terms: 1 + -2w + w2 = 4 + 1 Combine like terms: 4 + 1 = 5 1 + -2w + w2 = 5 Factor a perfect square on the left side: (w + -1)(w + -1) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (w + -1) equal to 2.236067978 and -2.236067978.Subproblem 1
w + -1 = 2.236067978 Simplifying w + -1 = 2.236067978 Reorder the terms: -1 + w = 2.236067978 Solving -1 + w = 2.236067978 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = 2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + w = 2.236067978 + 1 w = 2.236067978 + 1 Combine like terms: 2.236067978 + 1 = 3.236067978 w = 3.236067978 Simplifying w = 3.236067978Subproblem 2
w + -1 = -2.236067978 Simplifying w + -1 = -2.236067978 Reorder the terms: -1 + w = -2.236067978 Solving -1 + w = -2.236067978 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = -2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + w = -2.236067978 + 1 w = -2.236067978 + 1 Combine like terms: -2.236067978 + 1 = -1.236067978 w = -1.236067978 Simplifying w = -1.236067978Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.236067978, -1.236067978}
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