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Simplifying w(w + 4) = w + -5w + 16 Reorder the terms: w(4 + w) = w + -5w + 16 (4 * w + w * w) = w + -5w + 16 (4w + w2) = w + -5w + 16 Reorder the terms: 4w + w2 = 16 + w + -5w Combine like terms: w + -5w = -4w 4w + w2 = 16 + -4w Solving 4w + w2 = 16 + -4w Solving for variable 'w'. Reorder the terms: -16 + 4w + 4w + w2 = 16 + -4w + -16 + 4w Combine like terms: 4w + 4w = 8w -16 + 8w + w2 = 16 + -4w + -16 + 4w Reorder the terms: -16 + 8w + w2 = 16 + -16 + -4w + 4w Combine like terms: 16 + -16 = 0 -16 + 8w + w2 = 0 + -4w + 4w -16 + 8w + w2 = -4w + 4w Combine like terms: -4w + 4w = 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 = 1.656854249 w = 1.656854249 Simplifying w = 1.656854249Subproblem 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 = -9.656854249 w = -9.656854249 Simplifying w = -9.656854249Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.656854249, -9.656854249}
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