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Simplifying 2(2x4 + 27x2 + -81) = 0 Reorder the terms: 2(-81 + 27x2 + 2x4) = 0 (-81 * 2 + 27x2 * 2 + 2x4 * 2) = 0 (-162 + 54x2 + 4x4) = 0 Solving -162 + 54x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-81 + 27x2 + 2x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-81 + 27x2 + 2x4)' equal to zero and attempt to solve: Simplifying -81 + 27x2 + 2x4 = 0 Solving -81 + 27x2 + 2x4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -40.5 + 13.5x2 + x4 = 0 Move the constant term to the right: Add '40.5' to each side of the equation. -40.5 + 13.5x2 + 40.5 + x4 = 0 + 40.5 Reorder the terms: -40.5 + 40.5 + 13.5x2 + x4 = 0 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + 13.5x2 + x4 = 0 + 40.5 13.5x2 + x4 = 0 + 40.5 Combine like terms: 0 + 40.5 = 40.5 13.5x2 + x4 = 40.5 The x term is 13.5x2. Take half its coefficient (6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. 13.5x2 + 45.5625 + x4 = 40.5 + 45.5625 Reorder the terms: 45.5625 + 13.5x2 + x4 = 40.5 + 45.5625 Combine like terms: 40.5 + 45.5625 = 86.0625 45.5625 + 13.5x2 + x4 = 86.0625 Factor a perfect square on the left side: (x2 + 6.75)(x2 + 6.75) = 86.0625 Calculate the square root of the right side: 9.276987658 Break this problem into two subproblems by setting (x2 + 6.75) equal to 9.276987658 and -9.276987658.Subproblem 1
x2 + 6.75 = 9.276987658 Simplifying x2 + 6.75 = 9.276987658 Reorder the terms: 6.75 + x2 = 9.276987658 Solving 6.75 + x2 = 9.276987658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + x2 = 9.276987658 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x2 = 9.276987658 + -6.75 x2 = 9.276987658 + -6.75 Combine like terms: 9.276987658 + -6.75 = 2.526987658 x2 = 2.526987658 Simplifying x2 = 2.526987658 Take the square root of each side: x = {-1.589650168, 1.589650168}Subproblem 2
x2 + 6.75 = -9.276987658 Simplifying x2 + 6.75 = -9.276987658 Reorder the terms: 6.75 + x2 = -9.276987658 Solving 6.75 + x2 = -9.276987658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + x2 = -9.276987658 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x2 = -9.276987658 + -6.75 x2 = -9.276987658 + -6.75 Combine like terms: -9.276987658 + -6.75 = -16.026987658 x2 = -16.026987658 Simplifying x2 = -16.026987658 Reorder the terms: 16.026987658 + x2 = -16.026987658 + 16.026987658 Combine like terms: -16.026987658 + 16.026987658 = 0.000000000 16.026987658 + x2 = 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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