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Simplifying w2 + -74w + 330 = 0 Reorder the terms: 330 + -74w + w2 = 0 Solving 330 + -74w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-330' to each side of the equation. 330 + -74w + -330 + w2 = 0 + -330 Reorder the terms: 330 + -330 + -74w + w2 = 0 + -330 Combine like terms: 330 + -330 = 0 0 + -74w + w2 = 0 + -330 -74w + w2 = 0 + -330 Combine like terms: 0 + -330 = -330 -74w + w2 = -330 The w term is -74w. Take half its coefficient (-37). Square it (1369) and add it to both sides. Add '1369' to each side of the equation. -74w + 1369 + w2 = -330 + 1369 Reorder the terms: 1369 + -74w + w2 = -330 + 1369 Combine like terms: -330 + 1369 = 1039 1369 + -74w + w2 = 1039 Factor a perfect square on the left side: (w + -37)(w + -37) = 1039 Calculate the square root of the right side: 32.233522923 Break this problem into two subproblems by setting (w + -37) equal to 32.233522923 and -32.233522923.Subproblem 1
w + -37 = 32.233522923 Simplifying w + -37 = 32.233522923 Reorder the terms: -37 + w = 32.233522923 Solving -37 + w = 32.233522923 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '37' to each side of the equation. -37 + 37 + w = 32.233522923 + 37 Combine like terms: -37 + 37 = 0 0 + w = 32.233522923 + 37 w = 32.233522923 + 37 Combine like terms: 32.233522923 + 37 = 69.233522923 w = 69.233522923 Simplifying w = 69.233522923Subproblem 2
w + -37 = -32.233522923 Simplifying w + -37 = -32.233522923 Reorder the terms: -37 + w = -32.233522923 Solving -37 + w = -32.233522923 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '37' to each side of the equation. -37 + 37 + w = -32.233522923 + 37 Combine like terms: -37 + 37 = 0 0 + w = -32.233522923 + 37 w = -32.233522923 + 37 Combine like terms: -32.233522923 + 37 = 4.766477077 w = 4.766477077 Simplifying w = 4.766477077Solution
The solution to the problem is based on the solutions from the subproblems. w = {69.233522923, 4.766477077}
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