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Simplifying 2x4 + 16 + 32x2 = 0 Reorder the terms: 16 + 32x2 + 2x4 = 0 Solving 16 + 32x2 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + 16x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + 16x2 + x4)' equal to zero and attempt to solve: Simplifying 8 + 16x2 + x4 = 0 Solving 8 + 16x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 16x2 + -8 + x4 = 0 + -8 Reorder the terms: 8 + -8 + 16x2 + x4 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 16x2 + x4 = 0 + -8 16x2 + x4 = 0 + -8 Combine like terms: 0 + -8 = -8 16x2 + x4 = -8 The x term is 16x2. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x2 + 64 + x4 = -8 + 64 Reorder the terms: 64 + 16x2 + x4 = -8 + 64 Combine like terms: -8 + 64 = 56 64 + 16x2 + x4 = 56 Factor a perfect square on the left side: (x2 + 8)(x2 + 8) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (x2 + 8) equal to 7.483314774 and -7.483314774.Subproblem 1
x2 + 8 = 7.483314774 Simplifying x2 + 8 = 7.483314774 Reorder the terms: 8 + x2 = 7.483314774 Solving 8 + x2 = 7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x2 = 7.483314774 + -8 Combine like terms: 8 + -8 = 0 0 + x2 = 7.483314774 + -8 x2 = 7.483314774 + -8 Combine like terms: 7.483314774 + -8 = -0.516685226 x2 = -0.516685226 Simplifying x2 = -0.516685226 Reorder the terms: 0.516685226 + x2 = -0.516685226 + 0.516685226 Combine like terms: -0.516685226 + 0.516685226 = 0.000000000 0.516685226 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 8 = -7.483314774 Simplifying x2 + 8 = -7.483314774 Reorder the terms: 8 + x2 = -7.483314774 Solving 8 + x2 = -7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x2 = -7.483314774 + -8 Combine like terms: 8 + -8 = 0 0 + x2 = -7.483314774 + -8 x2 = -7.483314774 + -8 Combine like terms: -7.483314774 + -8 = -15.483314774 x2 = -15.483314774 Simplifying x2 = -15.483314774 Reorder the terms: 15.483314774 + x2 = -15.483314774 + 15.483314774 Combine like terms: -15.483314774 + 15.483314774 = 0.000000000 15.483314774 + 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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