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Simplifying w4 + 4w2 + -100 = 0 Reorder the terms: -100 + 4w2 + w4 = 0 Solving -100 + 4w2 + w4 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 4w2 + 100 + w4 = 0 + 100 Reorder the terms: -100 + 100 + 4w2 + w4 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 4w2 + w4 = 0 + 100 4w2 + w4 = 0 + 100 Combine like terms: 0 + 100 = 100 4w2 + w4 = 100 The w term is 4w2. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4w2 + 4 + w4 = 100 + 4 Reorder the terms: 4 + 4w2 + w4 = 100 + 4 Combine like terms: 100 + 4 = 104 4 + 4w2 + w4 = 104 Factor a perfect square on the left side: (w2 + 2)(w2 + 2) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (w2 + 2) equal to 10.198039027 and -10.198039027.Subproblem 1
w2 + 2 = 10.198039027 Simplifying w2 + 2 = 10.198039027 Reorder the terms: 2 + w2 = 10.198039027 Solving 2 + w2 = 10.198039027 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w2 = 10.198039027 + -2 Combine like terms: 2 + -2 = 0 0 + w2 = 10.198039027 + -2 w2 = 10.198039027 + -2 Combine like terms: 10.198039027 + -2 = 8.198039027 w2 = 8.198039027 Simplifying w2 = 8.198039027 Take the square root of each side: w = {-2.863221791, 2.863221791}Subproblem 2
w2 + 2 = -10.198039027 Simplifying w2 + 2 = -10.198039027 Reorder the terms: 2 + w2 = -10.198039027 Solving 2 + w2 = -10.198039027 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w2 = -10.198039027 + -2 Combine like terms: 2 + -2 = 0 0 + w2 = -10.198039027 + -2 w2 = -10.198039027 + -2 Combine like terms: -10.198039027 + -2 = -12.198039027 w2 = -12.198039027 Simplifying w2 = -12.198039027 Reorder the terms: 12.198039027 + w2 = -12.198039027 + 12.198039027 Combine like terms: -12.198039027 + 12.198039027 = 0.000000000 12.198039027 + 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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