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Simplifying 2w2 + 11w + -70 = 0 Reorder the terms: -70 + 11w + 2w2 = 0 Solving -70 + 11w + 2w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -35 + 5.5w + w2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + 5.5w + 35 + w2 = 0 + 35 Reorder the terms: -35 + 35 + 5.5w + w2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 5.5w + w2 = 0 + 35 5.5w + w2 = 0 + 35 Combine like terms: 0 + 35 = 35 5.5w + w2 = 35 The w term is 5.5w. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5w + 7.5625 + w2 = 35 + 7.5625 Reorder the terms: 7.5625 + 5.5w + w2 = 35 + 7.5625 Combine like terms: 35 + 7.5625 = 42.5625 7.5625 + 5.5w + w2 = 42.5625 Factor a perfect square on the left side: (w + 2.75)(w + 2.75) = 42.5625 Calculate the square root of the right side: 6.523994175 Break this problem into two subproblems by setting (w + 2.75) equal to 6.523994175 and -6.523994175.Subproblem 1
w + 2.75 = 6.523994175 Simplifying w + 2.75 = 6.523994175 Reorder the terms: 2.75 + w = 6.523994175 Solving 2.75 + w = 6.523994175 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + w = 6.523994175 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + w = 6.523994175 + -2.75 w = 6.523994175 + -2.75 Combine like terms: 6.523994175 + -2.75 = 3.773994175 w = 3.773994175 Simplifying w = 3.773994175Subproblem 2
w + 2.75 = -6.523994175 Simplifying w + 2.75 = -6.523994175 Reorder the terms: 2.75 + w = -6.523994175 Solving 2.75 + w = -6.523994175 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + w = -6.523994175 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + w = -6.523994175 + -2.75 w = -6.523994175 + -2.75 Combine like terms: -6.523994175 + -2.75 = -9.273994175 w = -9.273994175 Simplifying w = -9.273994175Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.773994175, -9.273994175}
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