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Simplifying 4w4 + 4w2 + -44 = 0 Reorder the terms: -44 + 4w2 + 4w4 = 0 Solving -44 + 4w2 + 4w4 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '4'. 4(-11 + w2 + w4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-11 + w2 + w4)' equal to zero and attempt to solve: Simplifying -11 + w2 + w4 = 0 Solving -11 + w2 + w4 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + w2 + 11 + w4 = 0 + 11 Reorder the terms: -11 + 11 + w2 + w4 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + w2 + w4 = 0 + 11 w2 + w4 = 0 + 11 Combine like terms: 0 + 11 = 11 w2 + w4 = 11 The w term is w2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. w2 + 0.25 + w4 = 11 + 0.25 Reorder the terms: 0.25 + w2 + w4 = 11 + 0.25 Combine like terms: 11 + 0.25 = 11.25 0.25 + w2 + w4 = 11.25 Factor a perfect square on the left side: (w2 + 0.5)(w2 + 0.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (w2 + 0.5) equal to 3.354101966 and -3.354101966.Subproblem 1
w2 + 0.5 = 3.354101966 Simplifying w2 + 0.5 = 3.354101966 Reorder the terms: 0.5 + w2 = 3.354101966 Solving 0.5 + w2 = 3.354101966 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w2 = 3.354101966 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w2 = 3.354101966 + -0.5 w2 = 3.354101966 + -0.5 Combine like terms: 3.354101966 + -0.5 = 2.854101966 w2 = 2.854101966 Simplifying w2 = 2.854101966 Take the square root of each side: w = {-1.689408762, 1.689408762}Subproblem 2
w2 + 0.5 = -3.354101966 Simplifying w2 + 0.5 = -3.354101966 Reorder the terms: 0.5 + w2 = -3.354101966 Solving 0.5 + w2 = -3.354101966 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w2 = -3.354101966 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w2 = -3.354101966 + -0.5 w2 = -3.354101966 + -0.5 Combine like terms: -3.354101966 + -0.5 = -3.854101966 w2 = -3.854101966 Simplifying w2 = -3.854101966 Reorder the terms: 3.854101966 + w2 = -3.854101966 + 3.854101966 Combine like terms: -3.854101966 + 3.854101966 = 0.000000000 3.854101966 + 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. 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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