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Simplifying 2w2 = (-7w + 3) Reorder the terms: 2w2 = (3 + -7w) Remove parenthesis around (3 + -7w) 2w2 = 3 + -7w Solving 2w2 = 3 + -7w Solving for variable 'w'. Reorder the terms: -3 + 7w + 2w2 = 3 + -7w + -3 + 7w Reorder the terms: -3 + 7w + 2w2 = 3 + -3 + -7w + 7w Combine like terms: 3 + -3 = 0 -3 + 7w + 2w2 = 0 + -7w + 7w -3 + 7w + 2w2 = -7w + 7w Combine like terms: -7w + 7w = 0 -3 + 7w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + 3.5w + w2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 3.5w + 1.5 + w2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 3.5w + w2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 3.5w + w2 = 0 + 1.5 3.5w + w2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 3.5w + w2 = 1.5 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 = 1.5 + 3.0625 Reorder the terms: 3.0625 + 3.5w + w2 = 1.5 + 3.0625 Combine like terms: 1.5 + 3.0625 = 4.5625 3.0625 + 3.5w + w2 = 4.5625 Factor a perfect square on the left side: (w + 1.75)(w + 1.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (w + 1.75) equal to 2.136000936 and -2.136000936.Subproblem 1
w + 1.75 = 2.136000936 Simplifying w + 1.75 = 2.136000936 Reorder the terms: 1.75 + w = 2.136000936 Solving 1.75 + w = 2.136000936 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 = 2.136000936 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + w = 2.136000936 + -1.75 w = 2.136000936 + -1.75 Combine like terms: 2.136000936 + -1.75 = 0.386000936 w = 0.386000936 Simplifying w = 0.386000936Subproblem 2
w + 1.75 = -2.136000936 Simplifying w + 1.75 = -2.136000936 Reorder the terms: 1.75 + w = -2.136000936 Solving 1.75 + w = -2.136000936 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 = -2.136000936 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + w = -2.136000936 + -1.75 w = -2.136000936 + -1.75 Combine like terms: -2.136000936 + -1.75 = -3.886000936 w = -3.886000936 Simplifying w = -3.886000936Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.386000936, -3.886000936}
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