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Simplifying (W + 3)(W + 3) = 2 Reorder the terms: (3 + W)(W + 3) = 2 Reorder the terms: (3 + W)(3 + W) = 2 Multiply (3 + W) * (3 + W) (3(3 + W) + W(3 + W)) = 2 ((3 * 3 + W * 3) + W(3 + W)) = 2 ((9 + 3W) + W(3 + W)) = 2 (9 + 3W + (3 * W + W * W)) = 2 (9 + 3W + (3W + W2)) = 2 Combine like terms: 3W + 3W = 6W (9 + 6W + W2) = 2 Solving 9 + 6W + W2 = 2 Solving for variable 'W'. Reorder the terms: 9 + -2 + 6W + W2 = 2 + -2 Combine like terms: 9 + -2 = 7 7 + 6W + W2 = 2 + -2 Combine like terms: 2 + -2 = 0 7 + 6W + W2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 6W + -7 + W2 = 0 + -7 Reorder the terms: 7 + -7 + 6W + W2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6W + W2 = 0 + -7 6W + W2 = 0 + -7 Combine like terms: 0 + -7 = -7 6W + W2 = -7 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 = -7 + 9 Reorder the terms: 9 + 6W + W2 = -7 + 9 Combine like terms: -7 + 9 = 2 9 + 6W + W2 = 2 Factor a perfect square on the left side: (W + 3)(W + 3) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (W + 3) equal to 1.414213562 and -1.414213562.Subproblem 1
W + 3 = 1.414213562 Simplifying W + 3 = 1.414213562 Reorder the terms: 3 + W = 1.414213562 Solving 3 + W = 1.414213562 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 = 1.414213562 + -3 Combine like terms: 3 + -3 = 0 0 + W = 1.414213562 + -3 W = 1.414213562 + -3 Combine like terms: 1.414213562 + -3 = -1.585786438 W = -1.585786438 Simplifying W = -1.585786438Subproblem 2
W + 3 = -1.414213562 Simplifying W + 3 = -1.414213562 Reorder the terms: 3 + W = -1.414213562 Solving 3 + W = -1.414213562 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 = -1.414213562 + -3 Combine like terms: 3 + -3 = 0 0 + W = -1.414213562 + -3 W = -1.414213562 + -3 Combine like terms: -1.414213562 + -3 = -4.414213562 W = -4.414213562 Simplifying W = -4.414213562Solution
The solution to the problem is based on the solutions from the subproblems. W = {-1.585786438, -4.414213562}
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