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Simplifying w2 + w = 126 Reorder the terms: w + w2 = 126 Solving w + w2 = 126 Solving for variable 'w'. Reorder the terms: -126 + w + w2 = 126 + -126 Combine like terms: 126 + -126 = 0 -126 + w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '126' to each side of the equation. -126 + w + 126 + w2 = 0 + 126 Reorder the terms: -126 + 126 + w + w2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + w + w2 = 0 + 126 w + w2 = 0 + 126 Combine like terms: 0 + 126 = 126 w + w2 = 126 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. w + 0.25 + w2 = 126 + 0.25 Reorder the terms: 0.25 + w + w2 = 126 + 0.25 Combine like terms: 126 + 0.25 = 126.25 0.25 + w + w2 = 126.25 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 126.25 Calculate the square root of the right side: 11.236102527 Break this problem into two subproblems by setting (w + 0.5) equal to 11.236102527 and -11.236102527.Subproblem 1
w + 0.5 = 11.236102527 Simplifying w + 0.5 = 11.236102527 Reorder the terms: 0.5 + w = 11.236102527 Solving 0.5 + w = 11.236102527 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 11.236102527 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 11.236102527 + -0.5 w = 11.236102527 + -0.5 Combine like terms: 11.236102527 + -0.5 = 10.736102527 w = 10.736102527 Simplifying w = 10.736102527Subproblem 2
w + 0.5 = -11.236102527 Simplifying w + 0.5 = -11.236102527 Reorder the terms: 0.5 + w = -11.236102527 Solving 0.5 + w = -11.236102527 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -11.236102527 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -11.236102527 + -0.5 w = -11.236102527 + -0.5 Combine like terms: -11.236102527 + -0.5 = -11.736102527 w = -11.736102527 Simplifying w = -11.736102527Solution
The solution to the problem is based on the solutions from the subproblems. w = {10.736102527, -11.736102527}
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