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Simplifying w2 + 8w = 380 Reorder the terms: 8w + w2 = 380 Solving 8w + w2 = 380 Solving for variable 'w'. Reorder the terms: -380 + 8w + w2 = 380 + -380 Combine like terms: 380 + -380 = 0 -380 + 8w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '380' to each side of the equation. -380 + 8w + 380 + w2 = 0 + 380 Reorder the terms: -380 + 380 + 8w + w2 = 0 + 380 Combine like terms: -380 + 380 = 0 0 + 8w + w2 = 0 + 380 8w + w2 = 0 + 380 Combine like terms: 0 + 380 = 380 8w + w2 = 380 The w term is 8w. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8w + 16 + w2 = 380 + 16 Reorder the terms: 16 + 8w + w2 = 380 + 16 Combine like terms: 380 + 16 = 396 16 + 8w + w2 = 396 Factor a perfect square on the left side: (w + 4)(w + 4) = 396 Calculate the square root of the right side: 19.899748742 Break this problem into two subproblems by setting (w + 4) equal to 19.899748742 and -19.899748742.Subproblem 1
w + 4 = 19.899748742 Simplifying w + 4 = 19.899748742 Reorder the terms: 4 + w = 19.899748742 Solving 4 + w = 19.899748742 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = 19.899748742 + -4 Combine like terms: 4 + -4 = 0 0 + w = 19.899748742 + -4 w = 19.899748742 + -4 Combine like terms: 19.899748742 + -4 = 15.899748742 w = 15.899748742 Simplifying w = 15.899748742Subproblem 2
w + 4 = -19.899748742 Simplifying w + 4 = -19.899748742 Reorder the terms: 4 + w = -19.899748742 Solving 4 + w = -19.899748742 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = -19.899748742 + -4 Combine like terms: 4 + -4 = 0 0 + w = -19.899748742 + -4 w = -19.899748742 + -4 Combine like terms: -19.899748742 + -4 = -23.899748742 w = -23.899748742 Simplifying w = -23.899748742Solution
The solution to the problem is based on the solutions from the subproblems. w = {15.899748742, -23.899748742}
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