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Simplifying 2w4 + -11w2 + 6 = 0 Reorder the terms: 6 + -11w2 + 2w4 = 0 Solving 6 + -11w2 + 2w4 = 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'. 3 + -5.5w2 + w4 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -5.5w2 + -3 + w4 = 0 + -3 Reorder the terms: 3 + -3 + -5.5w2 + w4 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5.5w2 + w4 = 0 + -3 -5.5w2 + w4 = 0 + -3 Combine like terms: 0 + -3 = -3 -5.5w2 + w4 = -3 The w term is -5.5w2. 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. -5.5w2 + 7.5625 + w4 = -3 + 7.5625 Reorder the terms: 7.5625 + -5.5w2 + w4 = -3 + 7.5625 Combine like terms: -3 + 7.5625 = 4.5625 7.5625 + -5.5w2 + w4 = 4.5625 Factor a perfect square on the left side: (w2 + -2.75)(w2 + -2.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (w2 + -2.75) equal to 2.136000936 and -2.136000936.Subproblem 1
w2 + -2.75 = 2.136000936 Simplifying w2 + -2.75 = 2.136000936 Reorder the terms: -2.75 + w2 = 2.136000936 Solving -2.75 + w2 = 2.136000936 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 + w2 = 2.136000936 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + w2 = 2.136000936 + 2.75 w2 = 2.136000936 + 2.75 Combine like terms: 2.136000936 + 2.75 = 4.886000936 w2 = 4.886000936 Simplifying w2 = 4.886000936 Take the square root of each side: w = {-2.210430034, 2.210430034}Subproblem 2
w2 + -2.75 = -2.136000936 Simplifying w2 + -2.75 = -2.136000936 Reorder the terms: -2.75 + w2 = -2.136000936 Solving -2.75 + w2 = -2.136000936 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 + w2 = -2.136000936 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + w2 = -2.136000936 + 2.75 w2 = -2.136000936 + 2.75 Combine like terms: -2.136000936 + 2.75 = 0.613999064 w2 = 0.613999064 Simplifying w2 = 0.613999064 Take the square root of each side: w = {-0.783580924, 0.783580924}Solution
The solution to the problem is based on the solutions from the subproblems. w = {-2.210430034, 2.210430034, -0.783580924, 0.783580924}
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