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Simplifying 196 = (W + 2)(2W + 2) Reorder the terms: 196 = (2 + W)(2W + 2) Reorder the terms: 196 = (2 + W)(2 + 2W) Multiply (2 + W) * (2 + 2W) 196 = (2(2 + 2W) + W(2 + 2W)) 196 = ((2 * 2 + 2W * 2) + W(2 + 2W)) 196 = ((4 + 4W) + W(2 + 2W)) 196 = (4 + 4W + (2 * W + 2W * W)) 196 = (4 + 4W + (2W + 2W2)) Combine like terms: 4W + 2W = 6W 196 = (4 + 6W + 2W2) Solving 196 = 4 + 6W + 2W2 Solving for variable 'W'. Combine like terms: 196 + -4 = 192 192 + -6W + -2W2 = 4 + 6W + 2W2 + -4 + -6W + -2W2 Reorder the terms: 192 + -6W + -2W2 = 4 + -4 + 6W + -6W + 2W2 + -2W2 Combine like terms: 4 + -4 = 0 192 + -6W + -2W2 = 0 + 6W + -6W + 2W2 + -2W2 192 + -6W + -2W2 = 6W + -6W + 2W2 + -2W2 Combine like terms: 6W + -6W = 0 192 + -6W + -2W2 = 0 + 2W2 + -2W2 192 + -6W + -2W2 = 2W2 + -2W2 Combine like terms: 2W2 + -2W2 = 0 192 + -6W + -2W2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(96 + -3W + -1W2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(96 + -3W + -1W2)' equal to zero and attempt to solve: Simplifying 96 + -3W + -1W2 = 0 Solving 96 + -3W + -1W2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -96 + 3W + W2 = 0 Move the constant term to the right: Add '96' to each side of the equation. -96 + 3W + 96 + W2 = 0 + 96 Reorder the terms: -96 + 96 + 3W + W2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 3W + W2 = 0 + 96 3W + W2 = 0 + 96 Combine like terms: 0 + 96 = 96 3W + W2 = 96 The W term is 3W. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3W + 2.25 + W2 = 96 + 2.25 Reorder the terms: 2.25 + 3W + W2 = 96 + 2.25 Combine like terms: 96 + 2.25 = 98.25 2.25 + 3W + W2 = 98.25 Factor a perfect square on the left side: (W + 1.5)(W + 1.5) = 98.25 Calculate the square root of the right side: 9.912113801 Break this problem into two subproblems by setting (W + 1.5) equal to 9.912113801 and -9.912113801.Subproblem 1
W + 1.5 = 9.912113801 Simplifying W + 1.5 = 9.912113801 Reorder the terms: 1.5 + W = 9.912113801 Solving 1.5 + W = 9.912113801 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + W = 9.912113801 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + W = 9.912113801 + -1.5 W = 9.912113801 + -1.5 Combine like terms: 9.912113801 + -1.5 = 8.412113801 W = 8.412113801 Simplifying W = 8.412113801Subproblem 2
W + 1.5 = -9.912113801 Simplifying W + 1.5 = -9.912113801 Reorder the terms: 1.5 + W = -9.912113801 Solving 1.5 + W = -9.912113801 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + W = -9.912113801 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + W = -9.912113801 + -1.5 W = -9.912113801 + -1.5 Combine like terms: -9.912113801 + -1.5 = -11.412113801 W = -11.412113801 Simplifying W = -11.412113801Solution
The solution to the problem is based on the solutions from the subproblems. W = {8.412113801, -11.412113801}Solution
W = {8.412113801, -11.412113801}
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