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Simplifying w2 + 23w + -126 = 0 Reorder the terms: -126 + 23w + w2 = 0 Solving -126 + 23w + 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 + 23w + 126 + w2 = 0 + 126 Reorder the terms: -126 + 126 + 23w + w2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + 23w + w2 = 0 + 126 23w + w2 = 0 + 126 Combine like terms: 0 + 126 = 126 23w + w2 = 126 The w term is 23w. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23w + 132.25 + w2 = 126 + 132.25 Reorder the terms: 132.25 + 23w + w2 = 126 + 132.25 Combine like terms: 126 + 132.25 = 258.25 132.25 + 23w + w2 = 258.25 Factor a perfect square on the left side: (w + 11.5)(w + 11.5) = 258.25 Calculate the square root of the right side: 16.07015868 Break this problem into two subproblems by setting (w + 11.5) equal to 16.07015868 and -16.07015868.Subproblem 1
w + 11.5 = 16.07015868 Simplifying w + 11.5 = 16.07015868 Reorder the terms: 11.5 + w = 16.07015868 Solving 11.5 + w = 16.07015868 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + w = 16.07015868 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + w = 16.07015868 + -11.5 w = 16.07015868 + -11.5 Combine like terms: 16.07015868 + -11.5 = 4.57015868 w = 4.57015868 Simplifying w = 4.57015868Subproblem 2
w + 11.5 = -16.07015868 Simplifying w + 11.5 = -16.07015868 Reorder the terms: 11.5 + w = -16.07015868 Solving 11.5 + w = -16.07015868 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + w = -16.07015868 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + w = -16.07015868 + -11.5 w = -16.07015868 + -11.5 Combine like terms: -16.07015868 + -11.5 = -27.57015868 w = -27.57015868 Simplifying w = -27.57015868Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.57015868, -27.57015868}
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