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Simplifying w2 + 30w = -41 Reorder the terms: 30w + w2 = -41 Solving 30w + w2 = -41 Solving for variable 'w'. Reorder the terms: 41 + 30w + w2 = -41 + 41 Combine like terms: -41 + 41 = 0 41 + 30w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + 30w + -41 + w2 = 0 + -41 Reorder the terms: 41 + -41 + 30w + w2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + 30w + w2 = 0 + -41 30w + w2 = 0 + -41 Combine like terms: 0 + -41 = -41 30w + w2 = -41 The w term is 30w. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30w + 225 + w2 = -41 + 225 Reorder the terms: 225 + 30w + w2 = -41 + 225 Combine like terms: -41 + 225 = 184 225 + 30w + w2 = 184 Factor a perfect square on the left side: (w + 15)(w + 15) = 184 Calculate the square root of the right side: 13.564659966 Break this problem into two subproblems by setting (w + 15) equal to 13.564659966 and -13.564659966.Subproblem 1
w + 15 = 13.564659966 Simplifying w + 15 = 13.564659966 Reorder the terms: 15 + w = 13.564659966 Solving 15 + w = 13.564659966 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + w = 13.564659966 + -15 Combine like terms: 15 + -15 = 0 0 + w = 13.564659966 + -15 w = 13.564659966 + -15 Combine like terms: 13.564659966 + -15 = -1.435340034 w = -1.435340034 Simplifying w = -1.435340034Subproblem 2
w + 15 = -13.564659966 Simplifying w + 15 = -13.564659966 Reorder the terms: 15 + w = -13.564659966 Solving 15 + w = -13.564659966 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + w = -13.564659966 + -15 Combine like terms: 15 + -15 = 0 0 + w = -13.564659966 + -15 w = -13.564659966 + -15 Combine like terms: -13.564659966 + -15 = -28.564659966 w = -28.564659966 Simplifying w = -28.564659966Solution
The solution to the problem is based on the solutions from the subproblems. w = {-1.435340034, -28.564659966}
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