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Simplifying 2w2 + 9w = 2w + -4 Reorder the terms: 9w + 2w2 = 2w + -4 Reorder the terms: 9w + 2w2 = -4 + 2w Solving 9w + 2w2 = -4 + 2w Solving for variable 'w'. Reorder the terms: 4 + 9w + -2w + 2w2 = -4 + 2w + 4 + -2w Combine like terms: 9w + -2w = 7w 4 + 7w + 2w2 = -4 + 2w + 4 + -2w Reorder the terms: 4 + 7w + 2w2 = -4 + 4 + 2w + -2w Combine like terms: -4 + 4 = 0 4 + 7w + 2w2 = 0 + 2w + -2w 4 + 7w + 2w2 = 2w + -2w Combine like terms: 2w + -2w = 0 4 + 7w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + 3.5w + w2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 3.5w + -2 + w2 = 0 + -2 Reorder the terms: 2 + -2 + 3.5w + w2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3.5w + w2 = 0 + -2 3.5w + w2 = 0 + -2 Combine like terms: 0 + -2 = -2 3.5w + w2 = -2 The w term is 3.5w. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5w + 3.0625 + w2 = -2 + 3.0625 Reorder the terms: 3.0625 + 3.5w + w2 = -2 + 3.0625 Combine like terms: -2 + 3.0625 = 1.0625 3.0625 + 3.5w + w2 = 1.0625 Factor a perfect square on the left side: (w + 1.75)(w + 1.75) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (w + 1.75) equal to 1.030776406 and -1.030776406.Subproblem 1
w + 1.75 = 1.030776406 Simplifying w + 1.75 = 1.030776406 Reorder the terms: 1.75 + w = 1.030776406 Solving 1.75 + w = 1.030776406 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + w = 1.030776406 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + w = 1.030776406 + -1.75 w = 1.030776406 + -1.75 Combine like terms: 1.030776406 + -1.75 = -0.719223594 w = -0.719223594 Simplifying w = -0.719223594Subproblem 2
w + 1.75 = -1.030776406 Simplifying w + 1.75 = -1.030776406 Reorder the terms: 1.75 + w = -1.030776406 Solving 1.75 + w = -1.030776406 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + w = -1.030776406 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + w = -1.030776406 + -1.75 w = -1.030776406 + -1.75 Combine like terms: -1.030776406 + -1.75 = -2.780776406 w = -2.780776406 Simplifying w = -2.780776406Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.719223594, -2.780776406}
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