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Simplifying -2w(w + -7) + 8w + 3 = 0 Reorder the terms: -2w(-7 + w) + 8w + 3 = 0 (-7 * -2w + w * -2w) + 8w + 3 = 0 (14w + -2w2) + 8w + 3 = 0 Reorder the terms: 3 + 14w + 8w + -2w2 = 0 Combine like terms: 14w + 8w = 22w 3 + 22w + -2w2 = 0 Solving 3 + 22w + -2w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1.5 + -11w + w2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -11w + 1.5 + w2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -11w + w2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -11w + w2 = 0 + 1.5 -11w + w2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -11w + w2 = 1.5 The w term is -11w. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11w + 30.25 + w2 = 1.5 + 30.25 Reorder the terms: 30.25 + -11w + w2 = 1.5 + 30.25 Combine like terms: 1.5 + 30.25 = 31.75 30.25 + -11w + w2 = 31.75 Factor a perfect square on the left side: (w + -5.5)(w + -5.5) = 31.75 Calculate the square root of the right side: 5.634713835 Break this problem into two subproblems by setting (w + -5.5) equal to 5.634713835 and -5.634713835.Subproblem 1
w + -5.5 = 5.634713835 Simplifying w + -5.5 = 5.634713835 Reorder the terms: -5.5 + w = 5.634713835 Solving -5.5 + w = 5.634713835 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + w = 5.634713835 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + w = 5.634713835 + 5.5 w = 5.634713835 + 5.5 Combine like terms: 5.634713835 + 5.5 = 11.134713835 w = 11.134713835 Simplifying w = 11.134713835Subproblem 2
w + -5.5 = -5.634713835 Simplifying w + -5.5 = -5.634713835 Reorder the terms: -5.5 + w = -5.634713835 Solving -5.5 + w = -5.634713835 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + w = -5.634713835 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + w = -5.634713835 + 5.5 w = -5.634713835 + 5.5 Combine like terms: -5.634713835 + 5.5 = -0.134713835 w = -0.134713835 Simplifying w = -0.134713835Solution
The solution to the problem is based on the solutions from the subproblems. w = {11.134713835, -0.134713835}
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