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Simplifying w2 + 11w + -90 = 0 Reorder the terms: -90 + 11w + w2 = 0 Solving -90 + 11w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 11w + 90 + w2 = 0 + 90 Reorder the terms: -90 + 90 + 11w + w2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 11w + w2 = 0 + 90 11w + w2 = 0 + 90 Combine like terms: 0 + 90 = 90 11w + w2 = 90 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 = 90 + 30.25 Reorder the terms: 30.25 + 11w + w2 = 90 + 30.25 Combine like terms: 90 + 30.25 = 120.25 30.25 + 11w + w2 = 120.25 Factor a perfect square on the left side: (w + 5.5)(w + 5.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (w + 5.5) equal to 10.9658561 and -10.9658561.Subproblem 1
w + 5.5 = 10.9658561 Simplifying w + 5.5 = 10.9658561 Reorder the terms: 5.5 + w = 10.9658561 Solving 5.5 + w = 10.9658561 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 = 10.9658561 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + w = 10.9658561 + -5.5 w = 10.9658561 + -5.5 Combine like terms: 10.9658561 + -5.5 = 5.4658561 w = 5.4658561 Simplifying w = 5.4658561Subproblem 2
w + 5.5 = -10.9658561 Simplifying w + 5.5 = -10.9658561 Reorder the terms: 5.5 + w = -10.9658561 Solving 5.5 + w = -10.9658561 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 = -10.9658561 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + w = -10.9658561 + -5.5 w = -10.9658561 + -5.5 Combine like terms: -10.9658561 + -5.5 = -16.4658561 w = -16.4658561 Simplifying w = -16.4658561Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.4658561, -16.4658561}
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