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Simplifying w2 + 12w + 36 = 0.11111 Reorder the terms: 36 + 12w + w2 = 0.11111 Solving 36 + 12w + w2 = 0.11111 Solving for variable 'w'. Reorder the terms: 36 + -0.11111 + 12w + w2 = 0.11111 + -0.11111 Combine like terms: 36 + -0.11111 = 35.88889 35.88889 + 12w + w2 = 0.11111 + -0.11111 Combine like terms: 0.11111 + -0.11111 = 0.00000 35.88889 + 12w + w2 = 0.00000 Begin completing the square. Move the constant term to the right: Add '-35.88889' to each side of the equation. 35.88889 + 12w + -35.88889 + w2 = 0.00000 + -35.88889 Reorder the terms: 35.88889 + -35.88889 + 12w + w2 = 0.00000 + -35.88889 Combine like terms: 35.88889 + -35.88889 = 0.00000 0.00000 + 12w + w2 = 0.00000 + -35.88889 12w + w2 = 0.00000 + -35.88889 Combine like terms: 0.00000 + -35.88889 = -35.88889 12w + w2 = -35.88889 The w term is 12w. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12w + 36 + w2 = -35.88889 + 36 Reorder the terms: 36 + 12w + w2 = -35.88889 + 36 Combine like terms: -35.88889 + 36 = 0.11111 36 + 12w + w2 = 0.11111 Factor a perfect square on the left side: (w + 6)(w + 6) = 0.11111 Calculate the square root of the right side: 0.333331667 Break this problem into two subproblems by setting (w + 6) equal to 0.333331667 and -0.333331667.Subproblem 1
w + 6 = 0.333331667 Simplifying w + 6 = 0.333331667 Reorder the terms: 6 + w = 0.333331667 Solving 6 + w = 0.333331667 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + w = 0.333331667 + -6 Combine like terms: 6 + -6 = 0 0 + w = 0.333331667 + -6 w = 0.333331667 + -6 Combine like terms: 0.333331667 + -6 = -5.666668333 w = -5.666668333 Simplifying w = -5.666668333Subproblem 2
w + 6 = -0.333331667 Simplifying w + 6 = -0.333331667 Reorder the terms: 6 + w = -0.333331667 Solving 6 + w = -0.333331667 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + w = -0.333331667 + -6 Combine like terms: 6 + -6 = 0 0 + w = -0.333331667 + -6 w = -0.333331667 + -6 Combine like terms: -0.333331667 + -6 = -6.333331667 w = -6.333331667 Simplifying w = -6.333331667Solution
The solution to the problem is based on the solutions from the subproblems. w = {-5.666668333, -6.333331667}
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