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Simplifying w2 + -16 = 8w Reorder the terms: -16 + w2 = 8w Solving -16 + w2 = 8w Solving for variable 'w'. Reorder the terms: -16 + -8w + w2 = 8w + -8w Combine like terms: 8w + -8w = 0 -16 + -8w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -8w + 16 + w2 = 0 + 16 Reorder the terms: -16 + 16 + -8w + w2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -8w + w2 = 0 + 16 -8w + w2 = 0 + 16 Combine like terms: 0 + 16 = 16 -8w + w2 = 16 The w term is -8w. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8w + 16 + w2 = 16 + 16 Reorder the terms: 16 + -8w + w2 = 16 + 16 Combine like terms: 16 + 16 = 32 16 + -8w + w2 = 32 Factor a perfect square on the left side: (w + -4)(w + -4) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (w + -4) equal to 5.656854249 and -5.656854249.Subproblem 1
w + -4 = 5.656854249 Simplifying w + -4 = 5.656854249 Reorder the terms: -4 + w = 5.656854249 Solving -4 + w = 5.656854249 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = 5.656854249 + 4 Combine like terms: -4 + 4 = 0 0 + w = 5.656854249 + 4 w = 5.656854249 + 4 Combine like terms: 5.656854249 + 4 = 9.656854249 w = 9.656854249 Simplifying w = 9.656854249Subproblem 2
w + -4 = -5.656854249 Simplifying w + -4 = -5.656854249 Reorder the terms: -4 + w = -5.656854249 Solving -4 + w = -5.656854249 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = -5.656854249 + 4 Combine like terms: -4 + 4 = 0 0 + w = -5.656854249 + 4 w = -5.656854249 + 4 Combine like terms: -5.656854249 + 4 = -1.656854249 w = -1.656854249 Simplifying w = -1.656854249Solution
The solution to the problem is based on the solutions from the subproblems. w = {9.656854249, -1.656854249}
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