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Simplifying w2 + -11w + -22 = 0 Reorder the terms: -22 + -11w + w2 = 0 Solving -22 + -11w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + -11w + 22 + w2 = 0 + 22 Reorder the terms: -22 + 22 + -11w + w2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -11w + w2 = 0 + 22 -11w + w2 = 0 + 22 Combine like terms: 0 + 22 = 22 -11w + w2 = 22 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 = 22 + 30.25 Reorder the terms: 30.25 + -11w + w2 = 22 + 30.25 Combine like terms: 22 + 30.25 = 52.25 30.25 + -11w + w2 = 52.25 Factor a perfect square on the left side: (w + -5.5)(w + -5.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (w + -5.5) equal to 7.228416147 and -7.228416147.Subproblem 1
w + -5.5 = 7.228416147 Simplifying w + -5.5 = 7.228416147 Reorder the terms: -5.5 + w = 7.228416147 Solving -5.5 + w = 7.228416147 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 = 7.228416147 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + w = 7.228416147 + 5.5 w = 7.228416147 + 5.5 Combine like terms: 7.228416147 + 5.5 = 12.728416147 w = 12.728416147 Simplifying w = 12.728416147Subproblem 2
w + -5.5 = -7.228416147 Simplifying w + -5.5 = -7.228416147 Reorder the terms: -5.5 + w = -7.228416147 Solving -5.5 + w = -7.228416147 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 = -7.228416147 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + w = -7.228416147 + 5.5 w = -7.228416147 + 5.5 Combine like terms: -7.228416147 + 5.5 = -1.728416147 w = -1.728416147 Simplifying w = -1.728416147Solution
The solution to the problem is based on the solutions from the subproblems. w = {12.728416147, -1.728416147}
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