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Simplifying w2 = 16 + -16w Solving w2 = 16 + -16w Solving for variable 'w'. Reorder the terms: -16 + 16w + w2 = 16 + -16w + -16 + 16w Reorder the terms: -16 + 16w + w2 = 16 + -16 + -16w + 16w Combine like terms: 16 + -16 = 0 -16 + 16w + w2 = 0 + -16w + 16w -16 + 16w + w2 = -16w + 16w Combine like terms: -16w + 16w = 0 -16 + 16w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 16w + 16 + w2 = 0 + 16 Reorder the terms: -16 + 16 + 16w + w2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 16w + w2 = 0 + 16 16w + w2 = 0 + 16 Combine like terms: 0 + 16 = 16 16w + w2 = 16 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 = 16 + 64 Reorder the terms: 64 + 16w + w2 = 16 + 64 Combine like terms: 16 + 64 = 80 64 + 16w + w2 = 80 Factor a perfect square on the left side: (w + 8)(w + 8) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (w + 8) equal to 8.94427191 and -8.94427191.Subproblem 1
w + 8 = 8.94427191 Simplifying w + 8 = 8.94427191 Reorder the terms: 8 + w = 8.94427191 Solving 8 + w = 8.94427191 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 = 8.94427191 + -8 Combine like terms: 8 + -8 = 0 0 + w = 8.94427191 + -8 w = 8.94427191 + -8 Combine like terms: 8.94427191 + -8 = 0.94427191 w = 0.94427191 Simplifying w = 0.94427191Subproblem 2
w + 8 = -8.94427191 Simplifying w + 8 = -8.94427191 Reorder the terms: 8 + w = -8.94427191 Solving 8 + w = -8.94427191 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 = -8.94427191 + -8 Combine like terms: 8 + -8 = 0 0 + w = -8.94427191 + -8 w = -8.94427191 + -8 Combine like terms: -8.94427191 + -8 = -16.94427191 w = -16.94427191 Simplifying w = -16.94427191Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.94427191, -16.94427191}
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