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Simplifying w2 + -4w + -126 = 0 Reorder the terms: -126 + -4w + w2 = 0 Solving -126 + -4w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '126' to each side of the equation. -126 + -4w + 126 + w2 = 0 + 126 Reorder the terms: -126 + 126 + -4w + w2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + -4w + w2 = 0 + 126 -4w + w2 = 0 + 126 Combine like terms: 0 + 126 = 126 -4w + w2 = 126 The w term is -4w. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4w + 4 + w2 = 126 + 4 Reorder the terms: 4 + -4w + w2 = 126 + 4 Combine like terms: 126 + 4 = 130 4 + -4w + w2 = 130 Factor a perfect square on the left side: (w + -2)(w + -2) = 130 Calculate the square root of the right side: 11.401754251 Break this problem into two subproblems by setting (w + -2) equal to 11.401754251 and -11.401754251.Subproblem 1
w + -2 = 11.401754251 Simplifying w + -2 = 11.401754251 Reorder the terms: -2 + w = 11.401754251 Solving -2 + w = 11.401754251 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = 11.401754251 + 2 Combine like terms: -2 + 2 = 0 0 + w = 11.401754251 + 2 w = 11.401754251 + 2 Combine like terms: 11.401754251 + 2 = 13.401754251 w = 13.401754251 Simplifying w = 13.401754251Subproblem 2
w + -2 = -11.401754251 Simplifying w + -2 = -11.401754251 Reorder the terms: -2 + w = -11.401754251 Solving -2 + w = -11.401754251 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = -11.401754251 + 2 Combine like terms: -2 + 2 = 0 0 + w = -11.401754251 + 2 w = -11.401754251 + 2 Combine like terms: -11.401754251 + 2 = -9.401754251 w = -9.401754251 Simplifying w = -9.401754251Solution
The solution to the problem is based on the solutions from the subproblems. w = {13.401754251, -9.401754251}
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