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Simplifying x4 + 16x2 + 4 = 0 Reorder the terms: 4 + 16x2 + x4 = 0 Solving 4 + 16x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 16x2 + -4 + x4 = 0 + -4 Reorder the terms: 4 + -4 + 16x2 + x4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 16x2 + x4 = 0 + -4 16x2 + x4 = 0 + -4 Combine like terms: 0 + -4 = -4 16x2 + x4 = -4 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 = -4 + 64 Reorder the terms: 64 + 16x2 + x4 = -4 + 64 Combine like terms: -4 + 64 = 60 64 + 16x2 + x4 = 60 Factor a perfect square on the left side: (x2 + 8)(x2 + 8) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x2 + 8) equal to 7.745966692 and -7.745966692.Subproblem 1
x2 + 8 = 7.745966692 Simplifying x2 + 8 = 7.745966692 Reorder the terms: 8 + x2 = 7.745966692 Solving 8 + x2 = 7.745966692 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 = 7.745966692 + -8 Combine like terms: 8 + -8 = 0 0 + x2 = 7.745966692 + -8 x2 = 7.745966692 + -8 Combine like terms: 7.745966692 + -8 = -0.254033308 x2 = -0.254033308 Simplifying x2 = -0.254033308 Reorder the terms: 0.254033308 + x2 = -0.254033308 + 0.254033308 Combine like terms: -0.254033308 + 0.254033308 = 0.000000000 0.254033308 + 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 = -7.745966692 Simplifying x2 + 8 = -7.745966692 Reorder the terms: 8 + x2 = -7.745966692 Solving 8 + x2 = -7.745966692 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 = -7.745966692 + -8 Combine like terms: 8 + -8 = 0 0 + x2 = -7.745966692 + -8 x2 = -7.745966692 + -8 Combine like terms: -7.745966692 + -8 = -15.745966692 x2 = -15.745966692 Simplifying x2 = -15.745966692 Reorder the terms: 15.745966692 + x2 = -15.745966692 + 15.745966692 Combine like terms: -15.745966692 + 15.745966692 = 0.000000000 15.745966692 + 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.
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