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Simplifying w2 + 3w + -10540 = 0 Reorder the terms: -10540 + 3w + w2 = 0 Solving -10540 + 3w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '10540' to each side of the equation. -10540 + 3w + 10540 + w2 = 0 + 10540 Reorder the terms: -10540 + 10540 + 3w + w2 = 0 + 10540 Combine like terms: -10540 + 10540 = 0 0 + 3w + w2 = 0 + 10540 3w + w2 = 0 + 10540 Combine like terms: 0 + 10540 = 10540 3w + w2 = 10540 The w term is 3w. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3w + 2.25 + w2 = 10540 + 2.25 Reorder the terms: 2.25 + 3w + w2 = 10540 + 2.25 Combine like terms: 10540 + 2.25 = 10542.25 2.25 + 3w + w2 = 10542.25 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = 10542.25 Calculate the square root of the right side: 102.67545958 Break this problem into two subproblems by setting (w + 1.5) equal to 102.67545958 and -102.67545958.Subproblem 1
w + 1.5 = 102.67545958 Simplifying w + 1.5 = 102.67545958 Reorder the terms: 1.5 + w = 102.67545958 Solving 1.5 + w = 102.67545958 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = 102.67545958 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 102.67545958 + -1.5 w = 102.67545958 + -1.5 Combine like terms: 102.67545958 + -1.5 = 101.17545958 w = 101.17545958 Simplifying w = 101.17545958Subproblem 2
w + 1.5 = -102.67545958 Simplifying w + 1.5 = -102.67545958 Reorder the terms: 1.5 + w = -102.67545958 Solving 1.5 + w = -102.67545958 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = -102.67545958 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -102.67545958 + -1.5 w = -102.67545958 + -1.5 Combine like terms: -102.67545958 + -1.5 = -104.17545958 w = -104.17545958 Simplifying w = -104.17545958Solution
The solution to the problem is based on the solutions from the subproblems. w = {101.17545958, -104.17545958}
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