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Simplifying w2 + 5w + -1296 = 0 Reorder the terms: -1296 + 5w + w2 = 0 Solving -1296 + 5w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '1296' to each side of the equation. -1296 + 5w + 1296 + w2 = 0 + 1296 Reorder the terms: -1296 + 1296 + 5w + w2 = 0 + 1296 Combine like terms: -1296 + 1296 = 0 0 + 5w + w2 = 0 + 1296 5w + w2 = 0 + 1296 Combine like terms: 0 + 1296 = 1296 5w + w2 = 1296 The w term is 5w. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5w + 6.25 + w2 = 1296 + 6.25 Reorder the terms: 6.25 + 5w + w2 = 1296 + 6.25 Combine like terms: 1296 + 6.25 = 1302.25 6.25 + 5w + w2 = 1302.25 Factor a perfect square on the left side: (w + 2.5)(w + 2.5) = 1302.25 Calculate the square root of the right side: 36.086701152 Break this problem into two subproblems by setting (w + 2.5) equal to 36.086701152 and -36.086701152.Subproblem 1
w + 2.5 = 36.086701152 Simplifying w + 2.5 = 36.086701152 Reorder the terms: 2.5 + w = 36.086701152 Solving 2.5 + w = 36.086701152 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = 36.086701152 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = 36.086701152 + -2.5 w = 36.086701152 + -2.5 Combine like terms: 36.086701152 + -2.5 = 33.586701152 w = 33.586701152 Simplifying w = 33.586701152Subproblem 2
w + 2.5 = -36.086701152 Simplifying w + 2.5 = -36.086701152 Reorder the terms: 2.5 + w = -36.086701152 Solving 2.5 + w = -36.086701152 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = -36.086701152 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = -36.086701152 + -2.5 w = -36.086701152 + -2.5 Combine like terms: -36.086701152 + -2.5 = -38.586701152 w = -38.586701152 Simplifying w = -38.586701152Solution
The solution to the problem is based on the solutions from the subproblems. w = {33.586701152, -38.586701152}
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