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Simplifying 2w2 + 22w = 63 Reorder the terms: 22w + 2w2 = 63 Solving 22w + 2w2 = 63 Solving for variable 'w'. Reorder the terms: -63 + 22w + 2w2 = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + 22w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -31.5 + 11w + w2 = 0 Move the constant term to the right: Add '31.5' to each side of the equation. -31.5 + 11w + 31.5 + w2 = 0 + 31.5 Reorder the terms: -31.5 + 31.5 + 11w + w2 = 0 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + 11w + w2 = 0 + 31.5 11w + w2 = 0 + 31.5 Combine like terms: 0 + 31.5 = 31.5 11w + w2 = 31.5 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 = 31.5 + 30.25 Reorder the terms: 30.25 + 11w + w2 = 31.5 + 30.25 Combine like terms: 31.5 + 30.25 = 61.75 30.25 + 11w + w2 = 61.75 Factor a perfect square on the left side: (w + 5.5)(w + 5.5) = 61.75 Calculate the square root of the right side: 7.858116823 Break this problem into two subproblems by setting (w + 5.5) equal to 7.858116823 and -7.858116823.Subproblem 1
w + 5.5 = 7.858116823 Simplifying w + 5.5 = 7.858116823 Reorder the terms: 5.5 + w = 7.858116823 Solving 5.5 + w = 7.858116823 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 = 7.858116823 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + w = 7.858116823 + -5.5 w = 7.858116823 + -5.5 Combine like terms: 7.858116823 + -5.5 = 2.358116823 w = 2.358116823 Simplifying w = 2.358116823Subproblem 2
w + 5.5 = -7.858116823 Simplifying w + 5.5 = -7.858116823 Reorder the terms: 5.5 + w = -7.858116823 Solving 5.5 + w = -7.858116823 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 = -7.858116823 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + w = -7.858116823 + -5.5 w = -7.858116823 + -5.5 Combine like terms: -7.858116823 + -5.5 = -13.358116823 w = -13.358116823 Simplifying w = -13.358116823Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.358116823, -13.358116823}
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