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Simplifying w4 + 100w2 + 6.25 = 0 Reorder the terms: 6.25 + 100w2 + w4 = 0 Solving 6.25 + 100w2 + w4 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + 100w2 + -6.25 + w4 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + 100w2 + w4 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + 100w2 + w4 = 0 + -6.25 100w2 + w4 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 100w2 + w4 = -6.25 The w term is 100w2. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100w2 + 2500 + w4 = -6.25 + 2500 Reorder the terms: 2500 + 100w2 + w4 = -6.25 + 2500 Combine like terms: -6.25 + 2500 = 2493.75 2500 + 100w2 + w4 = 2493.75 Factor a perfect square on the left side: (w2 + 50)(w2 + 50) = 2493.75 Calculate the square root of the right side: 49.937460889 Break this problem into two subproblems by setting (w2 + 50) equal to 49.937460889 and -49.937460889.Subproblem 1
w2 + 50 = 49.937460889 Simplifying w2 + 50 = 49.937460889 Reorder the terms: 50 + w2 = 49.937460889 Solving 50 + w2 = 49.937460889 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + w2 = 49.937460889 + -50 Combine like terms: 50 + -50 = 0 0 + w2 = 49.937460889 + -50 w2 = 49.937460889 + -50 Combine like terms: 49.937460889 + -50 = -0.062539111 w2 = -0.062539111 Simplifying w2 = -0.062539111 Reorder the terms: 0.062539111 + w2 = -0.062539111 + 0.062539111 Combine like terms: -0.062539111 + 0.062539111 = 0.000000000 0.062539111 + w2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
w2 + 50 = -49.937460889 Simplifying w2 + 50 = -49.937460889 Reorder the terms: 50 + w2 = -49.937460889 Solving 50 + w2 = -49.937460889 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + w2 = -49.937460889 + -50 Combine like terms: 50 + -50 = 0 0 + w2 = -49.937460889 + -50 w2 = -49.937460889 + -50 Combine like terms: -49.937460889 + -50 = -99.937460889 w2 = -99.937460889 Simplifying w2 = -99.937460889 Reorder the terms: 99.937460889 + w2 = -99.937460889 + 99.937460889 Combine like terms: -99.937460889 + 99.937460889 = 0.000000000 99.937460889 + w2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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