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Simplifying w2 + 2w + -3600 = 0 Reorder the terms: -3600 + 2w + w2 = 0 Solving -3600 + 2w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '3600' to each side of the equation. -3600 + 2w + 3600 + w2 = 0 + 3600 Reorder the terms: -3600 + 3600 + 2w + w2 = 0 + 3600 Combine like terms: -3600 + 3600 = 0 0 + 2w + w2 = 0 + 3600 2w + w2 = 0 + 3600 Combine like terms: 0 + 3600 = 3600 2w + w2 = 3600 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 = 3600 + 1 Reorder the terms: 1 + 2w + w2 = 3600 + 1 Combine like terms: 3600 + 1 = 3601 1 + 2w + w2 = 3601 Factor a perfect square on the left side: (w + 1)(w + 1) = 3601 Calculate the square root of the right side: 60.008332755 Break this problem into two subproblems by setting (w + 1) equal to 60.008332755 and -60.008332755.Subproblem 1
w + 1 = 60.008332755 Simplifying w + 1 = 60.008332755 Reorder the terms: 1 + w = 60.008332755 Solving 1 + w = 60.008332755 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 = 60.008332755 + -1 Combine like terms: 1 + -1 = 0 0 + w = 60.008332755 + -1 w = 60.008332755 + -1 Combine like terms: 60.008332755 + -1 = 59.008332755 w = 59.008332755 Simplifying w = 59.008332755Subproblem 2
w + 1 = -60.008332755 Simplifying w + 1 = -60.008332755 Reorder the terms: 1 + w = -60.008332755 Solving 1 + w = -60.008332755 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 = -60.008332755 + -1 Combine like terms: 1 + -1 = 0 0 + w = -60.008332755 + -1 w = -60.008332755 + -1 Combine like terms: -60.008332755 + -1 = -61.008332755 w = -61.008332755 Simplifying w = -61.008332755Solution
The solution to the problem is based on the solutions from the subproblems. w = {59.008332755, -61.008332755}
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