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Simplifying w2 + -11w + -1200 = 0 Reorder the terms: -1200 + -11w + w2 = 0 Solving -1200 + -11w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '1200' to each side of the equation. -1200 + -11w + 1200 + w2 = 0 + 1200 Reorder the terms: -1200 + 1200 + -11w + w2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + -11w + w2 = 0 + 1200 -11w + w2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 -11w + w2 = 1200 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 = 1200 + 30.25 Reorder the terms: 30.25 + -11w + w2 = 1200 + 30.25 Combine like terms: 1200 + 30.25 = 1230.25 30.25 + -11w + w2 = 1230.25 Factor a perfect square on the left side: (w + -5.5)(w + -5.5) = 1230.25 Calculate the square root of the right side: 35.074919815 Break this problem into two subproblems by setting (w + -5.5) equal to 35.074919815 and -35.074919815.Subproblem 1
w + -5.5 = 35.074919815 Simplifying w + -5.5 = 35.074919815 Reorder the terms: -5.5 + w = 35.074919815 Solving -5.5 + w = 35.074919815 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 = 35.074919815 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + w = 35.074919815 + 5.5 w = 35.074919815 + 5.5 Combine like terms: 35.074919815 + 5.5 = 40.574919815 w = 40.574919815 Simplifying w = 40.574919815Subproblem 2
w + -5.5 = -35.074919815 Simplifying w + -5.5 = -35.074919815 Reorder the terms: -5.5 + w = -35.074919815 Solving -5.5 + w = -35.074919815 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 = -35.074919815 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + w = -35.074919815 + 5.5 w = -35.074919815 + 5.5 Combine like terms: -35.074919815 + 5.5 = -29.574919815 w = -29.574919815 Simplifying w = -29.574919815Solution
The solution to the problem is based on the solutions from the subproblems. w = {40.574919815, -29.574919815}
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