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Simplifying W2 + -3W + -3W + 9 + -27 = 0 Reorder the terms: 9 + -27 + -3W + -3W + W2 = 0 Combine like terms: 9 + -27 = -18 -18 + -3W + -3W + W2 = 0 Combine like terms: -3W + -3W = -6W -18 + -6W + W2 = 0 Solving -18 + -6W + W2 = 0 Solving for variable 'W'. Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -6W + 18 + W2 = 0 + 18 Reorder the terms: -18 + 18 + -6W + W2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -6W + W2 = 0 + 18 -6W + W2 = 0 + 18 Combine like terms: 0 + 18 = 18 -6W + W2 = 18 The W term is -6W. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6W + 9 + W2 = 18 + 9 Reorder the terms: 9 + -6W + W2 = 18 + 9 Combine like terms: 18 + 9 = 27 9 + -6W + W2 = 27 Factor a perfect square on the left side: (W + -3)(W + -3) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (W + -3) equal to 5.196152423 and -5.196152423.Subproblem 1
W + -3 = 5.196152423 Simplifying W + -3 = 5.196152423 Reorder the terms: -3 + W = 5.196152423 Solving -3 + W = 5.196152423 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + W = 5.196152423 + 3 Combine like terms: -3 + 3 = 0 0 + W = 5.196152423 + 3 W = 5.196152423 + 3 Combine like terms: 5.196152423 + 3 = 8.196152423 W = 8.196152423 Simplifying W = 8.196152423Subproblem 2
W + -3 = -5.196152423 Simplifying W + -3 = -5.196152423 Reorder the terms: -3 + W = -5.196152423 Solving -3 + W = -5.196152423 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + W = -5.196152423 + 3 Combine like terms: -3 + 3 = 0 0 + W = -5.196152423 + 3 W = -5.196152423 + 3 Combine like terms: -5.196152423 + 3 = -2.196152423 W = -2.196152423 Simplifying W = -2.196152423Solution
The solution to the problem is based on the solutions from the subproblems. W = {8.196152423, -2.196152423}
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