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Simplifying w2 + 4w + -16 = 0 Reorder the terms: -16 + 4w + w2 = 0 Solving -16 + 4w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 4w + 16 + w2 = 0 + 16 Reorder the terms: -16 + 16 + 4w + w2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 4w + w2 = 0 + 16 4w + w2 = 0 + 16 Combine like terms: 0 + 16 = 16 4w + w2 = 16 The w term is 4w. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4w + 4 + w2 = 16 + 4 Reorder the terms: 4 + 4w + w2 = 16 + 4 Combine like terms: 16 + 4 = 20 4 + 4w + w2 = 20 Factor a perfect square on the left side: (w + 2)(w + 2) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (w + 2) equal to 4.472135955 and -4.472135955.Subproblem 1
w + 2 = 4.472135955 Simplifying w + 2 = 4.472135955 Reorder the terms: 2 + w = 4.472135955 Solving 2 + w = 4.472135955 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 4.472135955 + -2 Combine like terms: 2 + -2 = 0 0 + w = 4.472135955 + -2 w = 4.472135955 + -2 Combine like terms: 4.472135955 + -2 = 2.472135955 w = 2.472135955 Simplifying w = 2.472135955Subproblem 2
w + 2 = -4.472135955 Simplifying w + 2 = -4.472135955 Reorder the terms: 2 + w = -4.472135955 Solving 2 + w = -4.472135955 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = -4.472135955 + -2 Combine like terms: 2 + -2 = 0 0 + w = -4.472135955 + -2 w = -4.472135955 + -2 Combine like terms: -4.472135955 + -2 = -6.472135955 w = -6.472135955 Simplifying w = -6.472135955Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.472135955, -6.472135955}
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