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Simplifying 4w4 + 40w2 + -22 = 0 Reorder the terms: -22 + 40w2 + 4w4 = 0 Solving -22 + 40w2 + 4w4 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-11 + 20w2 + 2w4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + 20w2 + 2w4)' equal to zero and attempt to solve: Simplifying -11 + 20w2 + 2w4 = 0 Solving -11 + 20w2 + 2w4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + 10w2 + w4 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 10w2 + 5.5 + w4 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 10w2 + w4 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 10w2 + w4 = 0 + 5.5 10w2 + w4 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 10w2 + w4 = 5.5 The w term is 10w2. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10w2 + 25 + w4 = 5.5 + 25 Reorder the terms: 25 + 10w2 + w4 = 5.5 + 25 Combine like terms: 5.5 + 25 = 30.5 25 + 10w2 + w4 = 30.5 Factor a perfect square on the left side: (w2 + 5)(w2 + 5) = 30.5 Calculate the square root of the right side: 5.522680509 Break this problem into two subproblems by setting (w2 + 5) equal to 5.522680509 and -5.522680509.Subproblem 1
w2 + 5 = 5.522680509 Simplifying w2 + 5 = 5.522680509 Reorder the terms: 5 + w2 = 5.522680509 Solving 5 + w2 = 5.522680509 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w2 = 5.522680509 + -5 Combine like terms: 5 + -5 = 0 0 + w2 = 5.522680509 + -5 w2 = 5.522680509 + -5 Combine like terms: 5.522680509 + -5 = 0.522680509 w2 = 0.522680509 Simplifying w2 = 0.522680509 Take the square root of each side: w = {-0.722966465, 0.722966465}Subproblem 2
w2 + 5 = -5.522680509 Simplifying w2 + 5 = -5.522680509 Reorder the terms: 5 + w2 = -5.522680509 Solving 5 + w2 = -5.522680509 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w2 = -5.522680509 + -5 Combine like terms: 5 + -5 = 0 0 + w2 = -5.522680509 + -5 w2 = -5.522680509 + -5 Combine like terms: -5.522680509 + -5 = -10.522680509 w2 = -10.522680509 Simplifying w2 = -10.522680509 Reorder the terms: 10.522680509 + w2 = -10.522680509 + 10.522680509 Combine like terms: -10.522680509 + 10.522680509 = 0.000000000 10.522680509 + 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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