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Simplifying 2w2 + 16w + -230 = 0 Reorder the terms: -230 + 16w + 2w2 = 0 Solving -230 + 16w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-115 + 8w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-115 + 8w + w2)' equal to zero and attempt to solve: Simplifying -115 + 8w + w2 = 0 Solving -115 + 8w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '115' to each side of the equation. -115 + 8w + 115 + w2 = 0 + 115 Reorder the terms: -115 + 115 + 8w + w2 = 0 + 115 Combine like terms: -115 + 115 = 0 0 + 8w + w2 = 0 + 115 8w + w2 = 0 + 115 Combine like terms: 0 + 115 = 115 8w + w2 = 115 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 = 115 + 16 Reorder the terms: 16 + 8w + w2 = 115 + 16 Combine like terms: 115 + 16 = 131 16 + 8w + w2 = 131 Factor a perfect square on the left side: (w + 4)(w + 4) = 131 Calculate the square root of the right side: 11.445523142 Break this problem into two subproblems by setting (w + 4) equal to 11.445523142 and -11.445523142.Subproblem 1
w + 4 = 11.445523142 Simplifying w + 4 = 11.445523142 Reorder the terms: 4 + w = 11.445523142 Solving 4 + w = 11.445523142 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 = 11.445523142 + -4 Combine like terms: 4 + -4 = 0 0 + w = 11.445523142 + -4 w = 11.445523142 + -4 Combine like terms: 11.445523142 + -4 = 7.445523142 w = 7.445523142 Simplifying w = 7.445523142Subproblem 2
w + 4 = -11.445523142 Simplifying w + 4 = -11.445523142 Reorder the terms: 4 + w = -11.445523142 Solving 4 + w = -11.445523142 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 = -11.445523142 + -4 Combine like terms: 4 + -4 = 0 0 + w = -11.445523142 + -4 w = -11.445523142 + -4 Combine like terms: -11.445523142 + -4 = -15.445523142 w = -15.445523142 Simplifying w = -15.445523142Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.445523142, -15.445523142}Solution
w = {7.445523142, -15.445523142}
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