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Simplifying 0 = 3w + 24 + w4 + 8w2 + 64 + -3w + -832 Reorder the terms: 0 = 24 + 64 + -832 + 3w + -3w + 8w2 + w4 Combine like terms: 24 + 64 = 88 0 = 88 + -832 + 3w + -3w + 8w2 + w4 Combine like terms: 88 + -832 = -744 0 = -744 + 3w + -3w + 8w2 + w4 Combine like terms: 3w + -3w = 0 0 = -744 + 0 + 8w2 + w4 0 = -744 + 8w2 + w4 Solving 0 = -744 + 8w2 + w4 Solving for variable 'w'. Combine like terms: 0 + 744 = 744 744 + -8w2 + -1w4 = -744 + 8w2 + w4 + 744 + -8w2 + -1w4 Reorder the terms: 744 + -8w2 + -1w4 = -744 + 744 + 8w2 + -8w2 + w4 + -1w4 Combine like terms: -744 + 744 = 0 744 + -8w2 + -1w4 = 0 + 8w2 + -8w2 + w4 + -1w4 744 + -8w2 + -1w4 = 8w2 + -8w2 + w4 + -1w4 Combine like terms: 8w2 + -8w2 = 0 744 + -8w2 + -1w4 = 0 + w4 + -1w4 744 + -8w2 + -1w4 = w4 + -1w4 Combine like terms: w4 + -1w4 = 0 744 + -8w2 + -1w4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -744 + 8w2 + w4 = 0 Move the constant term to the right: Add '744' to each side of the equation. -744 + 8w2 + 744 + w4 = 0 + 744 Reorder the terms: -744 + 744 + 8w2 + w4 = 0 + 744 Combine like terms: -744 + 744 = 0 0 + 8w2 + w4 = 0 + 744 8w2 + w4 = 0 + 744 Combine like terms: 0 + 744 = 744 8w2 + w4 = 744 The w term is 8w2. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8w2 + 16 + w4 = 744 + 16 Reorder the terms: 16 + 8w2 + w4 = 744 + 16 Combine like terms: 744 + 16 = 760 16 + 8w2 + w4 = 760 Factor a perfect square on the left side: (w2 + 4)(w2 + 4) = 760 Calculate the square root of the right side: 27.568097504 Break this problem into two subproblems by setting (w2 + 4) equal to 27.568097504 and -27.568097504.Subproblem 1
w2 + 4 = 27.568097504 Simplifying w2 + 4 = 27.568097504 Reorder the terms: 4 + w2 = 27.568097504 Solving 4 + w2 = 27.568097504 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w2 = 27.568097504 + -4 Combine like terms: 4 + -4 = 0 0 + w2 = 27.568097504 + -4 w2 = 27.568097504 + -4 Combine like terms: 27.568097504 + -4 = 23.568097504 w2 = 23.568097504 Simplifying w2 = 23.568097504 Take the square root of each side: w = {-4.854698498, 4.854698498}Subproblem 2
w2 + 4 = -27.568097504 Simplifying w2 + 4 = -27.568097504 Reorder the terms: 4 + w2 = -27.568097504 Solving 4 + w2 = -27.568097504 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w2 = -27.568097504 + -4 Combine like terms: 4 + -4 = 0 0 + w2 = -27.568097504 + -4 w2 = -27.568097504 + -4 Combine like terms: -27.568097504 + -4 = -31.568097504 w2 = -31.568097504 Simplifying w2 = -31.568097504 Reorder the terms: 31.568097504 + w2 = -31.568097504 + 31.568097504 Combine like terms: -31.568097504 + 31.568097504 = 0.000000000 31.568097504 + 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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