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Simplifying w2 + 16w = 112 Reorder the terms: 16w + w2 = 112 Solving 16w + w2 = 112 Solving for variable 'w'. Reorder the terms: -112 + 16w + w2 = 112 + -112 Combine like terms: 112 + -112 = 0 -112 + 16w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '112' to each side of the equation. -112 + 16w + 112 + w2 = 0 + 112 Reorder the terms: -112 + 112 + 16w + w2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + 16w + w2 = 0 + 112 16w + w2 = 0 + 112 Combine like terms: 0 + 112 = 112 16w + w2 = 112 The w term is 16w. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16w + 64 + w2 = 112 + 64 Reorder the terms: 64 + 16w + w2 = 112 + 64 Combine like terms: 112 + 64 = 176 64 + 16w + w2 = 176 Factor a perfect square on the left side: (w + 8)(w + 8) = 176 Calculate the square root of the right side: 13.266499161 Break this problem into two subproblems by setting (w + 8) equal to 13.266499161 and -13.266499161.Subproblem 1
w + 8 = 13.266499161 Simplifying w + 8 = 13.266499161 Reorder the terms: 8 + w = 13.266499161 Solving 8 + w = 13.266499161 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + w = 13.266499161 + -8 Combine like terms: 8 + -8 = 0 0 + w = 13.266499161 + -8 w = 13.266499161 + -8 Combine like terms: 13.266499161 + -8 = 5.266499161 w = 5.266499161 Simplifying w = 5.266499161Subproblem 2
w + 8 = -13.266499161 Simplifying w + 8 = -13.266499161 Reorder the terms: 8 + w = -13.266499161 Solving 8 + w = -13.266499161 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + w = -13.266499161 + -8 Combine like terms: 8 + -8 = 0 0 + w = -13.266499161 + -8 w = -13.266499161 + -8 Combine like terms: -13.266499161 + -8 = -21.266499161 w = -21.266499161 Simplifying w = -21.266499161Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.266499161, -21.266499161}
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