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Simplifying 4w4 + 10w2 + -44 = 0 Reorder the terms: -44 + 10w2 + 4w4 = 0 Solving -44 + 10w2 + 4w4 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-22 + 5w2 + 2w4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-22 + 5w2 + 2w4)' equal to zero and attempt to solve: Simplifying -22 + 5w2 + 2w4 = 0 Solving -22 + 5w2 + 2w4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -11 + 2.5w2 + w4 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + 2.5w2 + 11 + w4 = 0 + 11 Reorder the terms: -11 + 11 + 2.5w2 + w4 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 2.5w2 + w4 = 0 + 11 2.5w2 + w4 = 0 + 11 Combine like terms: 0 + 11 = 11 2.5w2 + w4 = 11 The w term is 2.5w2. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5w2 + 1.5625 + w4 = 11 + 1.5625 Reorder the terms: 1.5625 + 2.5w2 + w4 = 11 + 1.5625 Combine like terms: 11 + 1.5625 = 12.5625 1.5625 + 2.5w2 + w4 = 12.5625 Factor a perfect square on the left side: (w2 + 1.25)(w2 + 1.25) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (w2 + 1.25) equal to 3.54436172 and -3.54436172.Subproblem 1
w2 + 1.25 = 3.54436172 Simplifying w2 + 1.25 = 3.54436172 Reorder the terms: 1.25 + w2 = 3.54436172 Solving 1.25 + w2 = 3.54436172 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + w2 = 3.54436172 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + w2 = 3.54436172 + -1.25 w2 = 3.54436172 + -1.25 Combine like terms: 3.54436172 + -1.25 = 2.29436172 w2 = 2.29436172 Simplifying w2 = 2.29436172 Take the square root of each side: w = {-1.514715062, 1.514715062}Subproblem 2
w2 + 1.25 = -3.54436172 Simplifying w2 + 1.25 = -3.54436172 Reorder the terms: 1.25 + w2 = -3.54436172 Solving 1.25 + w2 = -3.54436172 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + w2 = -3.54436172 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + w2 = -3.54436172 + -1.25 w2 = -3.54436172 + -1.25 Combine like terms: -3.54436172 + -1.25 = -4.79436172 w2 = -4.79436172 Simplifying w2 = -4.79436172 Reorder the terms: 4.79436172 + w2 = -4.79436172 + 4.79436172 Combine like terms: -4.79436172 + 4.79436172 = 0.00000000 4.79436172 + w2 = 0.00000000 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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