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Simplifying (W + 3)(W + -2) = 180 Reorder the terms: (3 + W)(W + -2) = 180 Reorder the terms: (3 + W)(-2 + W) = 180 Multiply (3 + W) * (-2 + W) (3(-2 + W) + W(-2 + W)) = 180 ((-2 * 3 + W * 3) + W(-2 + W)) = 180 ((-6 + 3W) + W(-2 + W)) = 180 (-6 + 3W + (-2 * W + W * W)) = 180 (-6 + 3W + (-2W + W2)) = 180 Combine like terms: 3W + -2W = 1W (-6 + 1W + W2) = 180 Solving -6 + 1W + W2 = 180 Solving for variable 'W'. Reorder the terms: -6 + -180 + 1W + W2 = 180 + -180 Combine like terms: -6 + -180 = -186 -186 + 1W + W2 = 180 + -180 Combine like terms: 180 + -180 = 0 -186 + 1W + W2 = 0 Begin completing the square. Move the constant term to the right: Add '186' to each side of the equation. -186 + 1W + 186 + W2 = 0 + 186 Reorder the terms: -186 + 186 + 1W + W2 = 0 + 186 Combine like terms: -186 + 186 = 0 0 + 1W + W2 = 0 + 186 1W + W2 = 0 + 186 Combine like terms: 0 + 186 = 186 1W + W2 = 186 The W term is 1W. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. W + 0.25 + W2 = 186 + 0.25 Reorder the terms: 0.25 + W + W2 = 186 + 0.25 Combine like terms: 186 + 0.25 = 186.25 0.25 + W + W2 = 186.25 Factor a perfect square on the left side: (W + 0.5)(W + 0.5) = 186.25 Calculate the square root of the right side: 13.647344064 Break this problem into two subproblems by setting (W + 0.5) equal to 13.647344064 and -13.647344064.Subproblem 1
W + 0.5 = 13.647344064 Simplifying W + 0.5 = 13.647344064 Reorder the terms: 0.5 + W = 13.647344064 Solving 0.5 + W = 13.647344064 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + W = 13.647344064 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + W = 13.647344064 + -0.5 W = 13.647344064 + -0.5 Combine like terms: 13.647344064 + -0.5 = 13.147344064 W = 13.147344064 Simplifying W = 13.147344064Subproblem 2
W + 0.5 = -13.647344064 Simplifying W + 0.5 = -13.647344064 Reorder the terms: 0.5 + W = -13.647344064 Solving 0.5 + W = -13.647344064 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + W = -13.647344064 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + W = -13.647344064 + -0.5 W = -13.647344064 + -0.5 Combine like terms: -13.647344064 + -0.5 = -14.147344064 W = -14.147344064 Simplifying W = -14.147344064Solution
The solution to the problem is based on the solutions from the subproblems. W = {13.147344064, -14.147344064}
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