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Simplifying 4w2 + 2w = 126 Reorder the terms: 2w + 4w2 = 126 Solving 2w + 4w2 = 126 Solving for variable 'w'. Reorder the terms: -126 + 2w + 4w2 = 126 + -126 Combine like terms: 126 + -126 = 0 -126 + 2w + 4w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-63 + w + 2w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-63 + w + 2w2)' equal to zero and attempt to solve: Simplifying -63 + w + 2w2 = 0 Solving -63 + w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -31.5 + 0.5w + w2 = 0 Move the constant term to the right: Add '31.5' to each side of the equation. -31.5 + 0.5w + 31.5 + w2 = 0 + 31.5 Reorder the terms: -31.5 + 31.5 + 0.5w + w2 = 0 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + 0.5w + w2 = 0 + 31.5 0.5w + w2 = 0 + 31.5 Combine like terms: 0 + 31.5 = 31.5 0.5w + w2 = 31.5 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5w + 0.25 + w2 = 31.5 + 0.25 Reorder the terms: 0.25 + 0.5w + w2 = 31.5 + 0.25 Combine like terms: 31.5 + 0.25 = 31.75 0.25 + 0.5w + w2 = 31.75 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 31.75 Calculate the square root of the right side: 5.634713835 Break this problem into two subproblems by setting (w + 0.5) equal to 5.634713835 and -5.634713835.Subproblem 1
w + 0.5 = 5.634713835 Simplifying w + 0.5 = 5.634713835 Reorder the terms: 0.5 + w = 5.634713835 Solving 0.5 + w = 5.634713835 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 5.634713835 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 5.634713835 + -0.5 w = 5.634713835 + -0.5 Combine like terms: 5.634713835 + -0.5 = 5.134713835 w = 5.134713835 Simplifying w = 5.134713835Subproblem 2
w + 0.5 = -5.634713835 Simplifying w + 0.5 = -5.634713835 Reorder the terms: 0.5 + w = -5.634713835 Solving 0.5 + w = -5.634713835 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -5.634713835 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -5.634713835 + -0.5 w = -5.634713835 + -0.5 Combine like terms: -5.634713835 + -0.5 = -6.134713835 w = -6.134713835 Simplifying w = -6.134713835Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.134713835, -6.134713835}Solution
w = {5.134713835, -6.134713835}
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