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Simplifying w2 + 2w + -25 = 0 Reorder the terms: -25 + 2w + w2 = 0 Solving -25 + 2w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 2w + 25 + w2 = 0 + 25 Reorder the terms: -25 + 25 + 2w + w2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 2w + w2 = 0 + 25 2w + w2 = 0 + 25 Combine like terms: 0 + 25 = 25 2w + w2 = 25 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 = 25 + 1 Reorder the terms: 1 + 2w + w2 = 25 + 1 Combine like terms: 25 + 1 = 26 1 + 2w + w2 = 26 Factor a perfect square on the left side: (w + 1)(w + 1) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (w + 1) equal to 5.099019514 and -5.099019514.Subproblem 1
w + 1 = 5.099019514 Simplifying w + 1 = 5.099019514 Reorder the terms: 1 + w = 5.099019514 Solving 1 + w = 5.099019514 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 = 5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + w = 5.099019514 + -1 w = 5.099019514 + -1 Combine like terms: 5.099019514 + -1 = 4.099019514 w = 4.099019514 Simplifying w = 4.099019514Subproblem 2
w + 1 = -5.099019514 Simplifying w + 1 = -5.099019514 Reorder the terms: 1 + w = -5.099019514 Solving 1 + w = -5.099019514 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 = -5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + w = -5.099019514 + -1 w = -5.099019514 + -1 Combine like terms: -5.099019514 + -1 = -6.099019514 w = -6.099019514 Simplifying w = -6.099019514Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.099019514, -6.099019514}
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