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Simplifying 2w2 + -8w + 7 = w2 + -4 Reorder the terms: 7 + -8w + 2w2 = w2 + -4 Reorder the terms: 7 + -8w + 2w2 = -4 + w2 Solving 7 + -8w + 2w2 = -4 + w2 Solving for variable 'w'. Reorder the terms: 7 + 4 + -8w + 2w2 + -1w2 = -4 + w2 + 4 + -1w2 Combine like terms: 7 + 4 = 11 11 + -8w + 2w2 + -1w2 = -4 + w2 + 4 + -1w2 Combine like terms: 2w2 + -1w2 = 1w2 11 + -8w + 1w2 = -4 + w2 + 4 + -1w2 Reorder the terms: 11 + -8w + 1w2 = -4 + 4 + w2 + -1w2 Combine like terms: -4 + 4 = 0 11 + -8w + 1w2 = 0 + w2 + -1w2 11 + -8w + 1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 11 + -8w + 1w2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -8w + -11 + w2 = 0 + -11 Reorder the terms: 11 + -11 + -8w + w2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -8w + w2 = 0 + -11 -8w + w2 = 0 + -11 Combine like terms: 0 + -11 = -11 -8w + w2 = -11 The w term is -8w. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8w + 16 + w2 = -11 + 16 Reorder the terms: 16 + -8w + w2 = -11 + 16 Combine like terms: -11 + 16 = 5 16 + -8w + w2 = 5 Factor a perfect square on the left side: (w + -4)(w + -4) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (w + -4) equal to 2.236067978 and -2.236067978.Subproblem 1
w + -4 = 2.236067978 Simplifying w + -4 = 2.236067978 Reorder the terms: -4 + w = 2.236067978 Solving -4 + w = 2.236067978 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = 2.236067978 + 4 Combine like terms: -4 + 4 = 0 0 + w = 2.236067978 + 4 w = 2.236067978 + 4 Combine like terms: 2.236067978 + 4 = 6.236067978 w = 6.236067978 Simplifying w = 6.236067978Subproblem 2
w + -4 = -2.236067978 Simplifying w + -4 = -2.236067978 Reorder the terms: -4 + w = -2.236067978 Solving -4 + w = -2.236067978 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = -2.236067978 + 4 Combine like terms: -4 + 4 = 0 0 + w = -2.236067978 + 4 w = -2.236067978 + 4 Combine like terms: -2.236067978 + 4 = 1.763932022 w = 1.763932022 Simplifying w = 1.763932022Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.236067978, 1.763932022}
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