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Simplifying W2 + 7W + -20736 = 0 Reorder the terms: -20736 + 7W + W2 = 0 Solving -20736 + 7W + W2 = 0 Solving for variable 'W'. Begin completing the square. Move the constant term to the right: Add '20736' to each side of the equation. -20736 + 7W + 20736 + W2 = 0 + 20736 Reorder the terms: -20736 + 20736 + 7W + W2 = 0 + 20736 Combine like terms: -20736 + 20736 = 0 0 + 7W + W2 = 0 + 20736 7W + W2 = 0 + 20736 Combine like terms: 0 + 20736 = 20736 7W + W2 = 20736 The W term is 7W. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7W + 12.25 + W2 = 20736 + 12.25 Reorder the terms: 12.25 + 7W + W2 = 20736 + 12.25 Combine like terms: 20736 + 12.25 = 20748.25 12.25 + 7W + W2 = 20748.25 Factor a perfect square on the left side: (W + 3.5)(W + 3.5) = 20748.25 Calculate the square root of the right side: 144.042528442 Break this problem into two subproblems by setting (W + 3.5) equal to 144.042528442 and -144.042528442.Subproblem 1
W + 3.5 = 144.042528442 Simplifying W + 3.5 = 144.042528442 Reorder the terms: 3.5 + W = 144.042528442 Solving 3.5 + W = 144.042528442 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + W = 144.042528442 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + W = 144.042528442 + -3.5 W = 144.042528442 + -3.5 Combine like terms: 144.042528442 + -3.5 = 140.542528442 W = 140.542528442 Simplifying W = 140.542528442Subproblem 2
W + 3.5 = -144.042528442 Simplifying W + 3.5 = -144.042528442 Reorder the terms: 3.5 + W = -144.042528442 Solving 3.5 + W = -144.042528442 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + W = -144.042528442 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + W = -144.042528442 + -3.5 W = -144.042528442 + -3.5 Combine like terms: -144.042528442 + -3.5 = -147.542528442 W = -147.542528442 Simplifying W = -147.542528442Solution
The solution to the problem is based on the solutions from the subproblems. W = {140.542528442, -147.542528442}
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