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Simplifying w2 + 28w + 41 = 0 Reorder the terms: 41 + 28w + w2 = 0 Solving 41 + 28w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + 28w + -41 + w2 = 0 + -41 Reorder the terms: 41 + -41 + 28w + w2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + 28w + w2 = 0 + -41 28w + w2 = 0 + -41 Combine like terms: 0 + -41 = -41 28w + w2 = -41 The w term is 28w. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28w + 196 + w2 = -41 + 196 Reorder the terms: 196 + 28w + w2 = -41 + 196 Combine like terms: -41 + 196 = 155 196 + 28w + w2 = 155 Factor a perfect square on the left side: (w + 14)(w + 14) = 155 Calculate the square root of the right side: 12.449899598 Break this problem into two subproblems by setting (w + 14) equal to 12.449899598 and -12.449899598.Subproblem 1
w + 14 = 12.449899598 Simplifying w + 14 = 12.449899598 Reorder the terms: 14 + w = 12.449899598 Solving 14 + w = 12.449899598 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + w = 12.449899598 + -14 Combine like terms: 14 + -14 = 0 0 + w = 12.449899598 + -14 w = 12.449899598 + -14 Combine like terms: 12.449899598 + -14 = -1.550100402 w = -1.550100402 Simplifying w = -1.550100402Subproblem 2
w + 14 = -12.449899598 Simplifying w + 14 = -12.449899598 Reorder the terms: 14 + w = -12.449899598 Solving 14 + w = -12.449899598 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + w = -12.449899598 + -14 Combine like terms: 14 + -14 = 0 0 + w = -12.449899598 + -14 w = -12.449899598 + -14 Combine like terms: -12.449899598 + -14 = -26.449899598 w = -26.449899598 Simplifying w = -26.449899598Solution
The solution to the problem is based on the solutions from the subproblems. w = {-1.550100402, -26.449899598}
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