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Simplifying w2 + 12w = 31 Reorder the terms: 12w + w2 = 31 Solving 12w + w2 = 31 Solving for variable 'w'. Reorder the terms: -31 + 12w + w2 = 31 + -31 Combine like terms: 31 + -31 = 0 -31 + 12w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 12w + 31 + w2 = 0 + 31 Reorder the terms: -31 + 31 + 12w + w2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 12w + w2 = 0 + 31 12w + w2 = 0 + 31 Combine like terms: 0 + 31 = 31 12w + w2 = 31 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 = 31 + 36 Reorder the terms: 36 + 12w + w2 = 31 + 36 Combine like terms: 31 + 36 = 67 36 + 12w + w2 = 67 Factor a perfect square on the left side: (w + 6)(w + 6) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (w + 6) equal to 8.185352772 and -8.185352772.Subproblem 1
w + 6 = 8.185352772 Simplifying w + 6 = 8.185352772 Reorder the terms: 6 + w = 8.185352772 Solving 6 + w = 8.185352772 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 = 8.185352772 + -6 Combine like terms: 6 + -6 = 0 0 + w = 8.185352772 + -6 w = 8.185352772 + -6 Combine like terms: 8.185352772 + -6 = 2.185352772 w = 2.185352772 Simplifying w = 2.185352772Subproblem 2
w + 6 = -8.185352772 Simplifying w + 6 = -8.185352772 Reorder the terms: 6 + w = -8.185352772 Solving 6 + w = -8.185352772 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 = -8.185352772 + -6 Combine like terms: 6 + -6 = 0 0 + w = -8.185352772 + -6 w = -8.185352772 + -6 Combine like terms: -8.185352772 + -6 = -14.185352772 w = -14.185352772 Simplifying w = -14.185352772Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.185352772, -14.185352772}
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