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Simplifying 44w + 4w2 = 121 Solving 44w + 4w2 = 121 Solving for variable 'w'. Reorder the terms: -121 + 44w + 4w2 = 121 + -121 Combine like terms: 121 + -121 = 0 -121 + 44w + 4w2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -30.25 + 11w + w2 = 0 Move the constant term to the right: Add '30.25' to each side of the equation. -30.25 + 11w + 30.25 + w2 = 0 + 30.25 Reorder the terms: -30.25 + 30.25 + 11w + w2 = 0 + 30.25 Combine like terms: -30.25 + 30.25 = 0.00 0.00 + 11w + w2 = 0 + 30.25 11w + w2 = 0 + 30.25 Combine like terms: 0 + 30.25 = 30.25 11w + w2 = 30.25 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 = 30.25 + 30.25 Reorder the terms: 30.25 + 11w + w2 = 30.25 + 30.25 Combine like terms: 30.25 + 30.25 = 60.5 30.25 + 11w + w2 = 60.5 Factor a perfect square on the left side: (w + 5.5)(w + 5.5) = 60.5 Calculate the square root of the right side: 7.778174593 Break this problem into two subproblems by setting (w + 5.5) equal to 7.778174593 and -7.778174593.Subproblem 1
w + 5.5 = 7.778174593 Simplifying w + 5.5 = 7.778174593 Reorder the terms: 5.5 + w = 7.778174593 Solving 5.5 + w = 7.778174593 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 = 7.778174593 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + w = 7.778174593 + -5.5 w = 7.778174593 + -5.5 Combine like terms: 7.778174593 + -5.5 = 2.278174593 w = 2.278174593 Simplifying w = 2.278174593Subproblem 2
w + 5.5 = -7.778174593 Simplifying w + 5.5 = -7.778174593 Reorder the terms: 5.5 + w = -7.778174593 Solving 5.5 + w = -7.778174593 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 = -7.778174593 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + w = -7.778174593 + -5.5 w = -7.778174593 + -5.5 Combine like terms: -7.778174593 + -5.5 = -13.278174593 w = -13.278174593 Simplifying w = -13.278174593Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.278174593, -13.278174593}
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