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Simplifying (W + 3)(W + -2) = 156 Reorder the terms: (3 + W)(W + -2) = 156 Reorder the terms: (3 + W)(-2 + W) = 156 Multiply (3 + W) * (-2 + W) (3(-2 + W) + W(-2 + W)) = 156 ((-2 * 3 + W * 3) + W(-2 + W)) = 156 ((-6 + 3W) + W(-2 + W)) = 156 (-6 + 3W + (-2 * W + W * W)) = 156 (-6 + 3W + (-2W + W2)) = 156 Combine like terms: 3W + -2W = 1W (-6 + 1W + W2) = 156 Solving -6 + 1W + W2 = 156 Solving for variable 'W'. Reorder the terms: -6 + -156 + 1W + W2 = 156 + -156 Combine like terms: -6 + -156 = -162 -162 + 1W + W2 = 156 + -156 Combine like terms: 156 + -156 = 0 -162 + 1W + W2 = 0 Begin completing the square. Move the constant term to the right: Add '162' to each side of the equation. -162 + 1W + 162 + W2 = 0 + 162 Reorder the terms: -162 + 162 + 1W + W2 = 0 + 162 Combine like terms: -162 + 162 = 0 0 + 1W + W2 = 0 + 162 1W + W2 = 0 + 162 Combine like terms: 0 + 162 = 162 1W + W2 = 162 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 = 162 + 0.25 Reorder the terms: 0.25 + W + W2 = 162 + 0.25 Combine like terms: 162 + 0.25 = 162.25 0.25 + W + W2 = 162.25 Factor a perfect square on the left side: (W + 0.5)(W + 0.5) = 162.25 Calculate the square root of the right side: 12.737739203 Break this problem into two subproblems by setting (W + 0.5) equal to 12.737739203 and -12.737739203.Subproblem 1
W + 0.5 = 12.737739203 Simplifying W + 0.5 = 12.737739203 Reorder the terms: 0.5 + W = 12.737739203 Solving 0.5 + W = 12.737739203 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 = 12.737739203 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + W = 12.737739203 + -0.5 W = 12.737739203 + -0.5 Combine like terms: 12.737739203 + -0.5 = 12.237739203 W = 12.237739203 Simplifying W = 12.237739203Subproblem 2
W + 0.5 = -12.737739203 Simplifying W + 0.5 = -12.737739203 Reorder the terms: 0.5 + W = -12.737739203 Solving 0.5 + W = -12.737739203 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 = -12.737739203 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + W = -12.737739203 + -0.5 W = -12.737739203 + -0.5 Combine like terms: -12.737739203 + -0.5 = -13.237739203 W = -13.237739203 Simplifying W = -13.237739203Solution
The solution to the problem is based on the solutions from the subproblems. W = {12.237739203, -13.237739203}
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